Currently, moving timeline objects in and out of timeline groups is not possible, and requires deleting the group first and then creating a new group and possibly renaming it. Too convoluted for a task that should be a simple case of drag-and-drop.
Should be fairly self-explanatory but I'm including a screencast anyway. Sorry if I speak too slowly---English is not my first language!
This had previously been suggested on IdeaStation about 3 years ago, but the idea was archived due to lack of votes, since I've only used Fusion 360 for about 3 months, I didn't get to upvote that one, so I'm resurrecting it here.
I'd also like to propose groups within groups in the timeline. I realise this may not be considered "essential" but I"ve encountered situations where sub-groups would have made a lot of sense.