I'd like admins to be able to create different types of groups of users, and for those groups to be placed within a hierarchy.

For example, a marine detachment would be a group, and it would belong to a larger group, a regional command.

Each type of group has unique metadata associated with it.

Does a plugin for this exist? Or do I need to write one?

It seems the closest you'll get at the moment is Frontend User Roles manager though I'm not sure this suits your purpose.

Yeah, that's not quite what I need. Thanks for the thought, though!