Currently: the Groups you are a member of are listed last, at the very end, of your friends list when you are entered into the wonderful world of glitch, until you click on it... then they pop to the top.
In my opinion, they are not intuitively obvious to find when you start. I think many Glitch's are having a hard time finding familiar faces in game in which to socialize. The Help chat is the first thing you see when you enter. It has become somewhat bogged with friendly chatting which could be easily transferred to Group chat or PMs.
Solution: move the groups you are members in to the top of the friends list! Change the font color of the Groups Chats you are following at the moment. If you close/leave a Group chat, then the font color of that Group could change back to 'normal'.
Plus: when you have to reload the game and the group chat closes, it'll be easier to get back opened.