Showing/Hiding groups with "triangle flippities"
At least, that's what David Pogue calls them, and I think it's safe to rely on him as a source of terminology.
Basically what I want is what most programs, including Netbeans (screenshot) do. A bunch of stuff is hidden and shown by toggling a parent container.
I would have expected there to be a JThing for this, but there does not appear to be.
I've also looked at trees, but can't find a way of editing them to include components rather than text.