A problem I was having was that even though you could successfully create a new Task Force (Crtl-F4), create branches under it and assign Task Groups to it, in the Naval Organization window tab (F12), when you looked at the Task Force Organization window, the Task Group was still assigned to the Fleet Headquarters Task Force.   So when you select it under the branch it is assigned in the Naval Organization window tab and look at the Details and Special Orders area in the top left, the Task Force drop down shows it still being assigned to the Fleet Headquarters Task Force.   The solution: in the Initiative area below the Task Force drop down there is a Set button.   

1.     Select the Task Group that you have assigned to the branch under the new Task Force.   
2.     In the Task Force drop down, change the Task Force to the new Task Force that you have created.   
3.     Push the Set button in the Initiative area.   

Your Task Group under your new branch of your new Task Force should now show up correctly in the Task Force Organizations (Crtl-F4) window and whenever you select it in the Task Groups (F12) Naval Organizations Tab, the correct Task Force will show up in the Task Force drop down upper left corner of the Details and Special Orders area. 

You have to remember that this game is a work in progress, things are gonna be unpolished at times.
That being said, its not difficult its just a bit confusing. Using the Naval Organization tab to assign a ship to a task force does work, it just doesn't register on the task group window. The extra steps are needed to make it register correctly.

This will create a new Task Group called 1st Exploration Squadron with all ships in that group, and belonging to the Explorer Command Task Force.

Thanks for the clarification, Hawkeye.  One subtlety, though - it will have all the ships in the 1st Exploration Squadron branch that are colocated with the currently selected TG.  So if the squadron's ships are in Earth orbit but your currently selected TG is at Mars, this process will result in an empty TG.  This is why you should always click on one of the ships in the branch that you want first - that will change the currently selected TG to the one containing that ship, and you'll at least get that ship in the 1st Exploration Squadron TG.

John

Ah that is more clear.  It is just that I have been creating the task group first the dealing with the naval organizational chart second.  I have to change my way of doing things it seems.

John, I'm not sure I follow your advice exactly but I will play about a bit to see what I can accomplish.  At the moment I do the swap when the ICG hits earth and I can shuffle the ships over to "New Construction/Shakedown/Training" so I have only one ship in the task force.  I think what I need to do is add more branches to my organization tree and that may allow me to do what you suggest.  That naval organization tree isn't shall we say "intuitive."

I might detail my way of doing it a little further and it might help you as well.

I practically do as you do, I have a single construction TF where all ships gets assigned to when created.

I also have one "Reserve" TG for each Task-force where I then assign every resource that I want to belong to that particular Task-force. This TG is obviously created in such a way that it is part if that said Task-force. When I move a ship from my construction TG to the Reserve TG the ship will then automatically belong to that Task-force.

In the "Naval Organizational" tab I do not include this Reserve TG since it is quite dynamic. What I do is to create all the TG and subgroups of those TG. Some ships are more or less permanently assigned to certain TG others (like escorts) are assigned when needed using the "Naval Organizational" tab. I then create the TG from the "Naval Organizational" tab and I have my TG ready to sail off into space.

I also organize sub groups under each TG if it has escorts or scouting elements that often break of from the TG.

One example might be like this...

RD1 - 1st Independent Recon Division
  RD1 - 2nd Cruiser Squadron
    RD1 - 2nd Cruiser Squadron - #1   (element #1)
      CA RSS Juggernaught
      CA RSS Juggernaught - Hangar space
        RD1 - 2nd Cruiser Squadron - Scout #11  (Element #1, detachment #1)
          SC Scout01
        RD1 - 2nd Cruiser Squadron - Scout #12  (Element #1, detachment #2)
          SC Scout02
        RD1 - 2nd Cruiser Squadron - INT #13  (Element #1, detachment #2)
          INT Interceptor01
          INT Interceptor02
          INT Interceptor03
          INT Interceptor04
          INT Interceptor05
    RD1 - 2nd Cruiser Squadron - #2
      FF - Rodrigues
      FF - Sebastian
      FFL - Valasquez
  RD1 - 3rd Recon Squadron
    RD1 - 3rd Recon Squadron - #1
      CL RSS Benedict
      CL RSS Benedict - Hangar space
        RD1 - 3rd Recon Squadron - Recon #11
          SC - Scout03
    RD1 - 3rd Recon Squadron - #2
      CL RSS Rangoon
      CL RSS Rangoon - Hangar space
        RD1 - 3rd Recon Squadron - Recon #21
          SC - Scout04

etc...

I don't have to place ships in the structure all the time, but the base structure don't really change all that much. Some element might even be empty at time even on missions, but they are there and can be filled quickly when needed.

The first letters in my naming standard are basically for ease of finding TG in the TG drop down list, this way they are always sorted in Task-force then Task-group then Task-group elements and last Task-group detachments.

It also give me a sense of military discipline when I play.  
      

No, that is how you do it. It was what I tried to explain above but I was probably not coherent enough to make much sense.

You can, however, split up TG from this one and the new will belong to the same Task Force. Or if you have one TG selected and you press new the new will belong to the same task force as the selected TG. At least I think it work like that.

I usually make extensive use of the "Naval Organization" tab, it make things so much easier to manage in the long run. It make you much more sane to be able to sort out complex organization structure through this screen.

I basically have one Reserve force TG for each task force where I place ships that are currently not in use for that Task Force. In the Naval Organizational tag I draw up a Hierarchy of the TO&E and can the select the Reserve Force TG and place ships into the proper branches and simply create the TG with the right name and content quickly. Also work very well for fighter squadrons/wings etc..

In the Task Groups window, in the top left corner there's a Details and Special Orders section.  The bottom element of that group is a Task Force pulldown that you can use to change the Task Force to which a given Task Group is assigned.

Another point of information - as of a year or so ago this pull-down was bugged (when Steve put the TF organization tab in).  The process described of pulling a forming a new TG with the same ships from the TF organization tab was the correct one at that time.  I don't remember Steve announcing any changes to this procedure.

Note that I said "new TG".  My recollection is that there's no way to change an existing TG's TF - you create a new one with the same ships by using the TF organization tab.  So Paul saying "the task groups ... are still associated with the old one" leads me to think you're maybe not using the TF tab to create a new TG (the alternatives are imprecise language in what Paul means by "the task groups" or my recollection of this stuff being wrong ).

John