Questions about groups on THWACK

Is there a way to join groups on Thwack? There seem to be two group modes: those that require mods to invite you to, and those that are open for anyone to post in. Is that the way they generally work?

What is the relationship between groups and sub-groups? Most groups show an empty list when clicking on the sub-group link, but looking at sub-groups from within the Federal site goes to, which appears to show most of Thwack's public groups.