With this core framework in place you can see how groups can be used to bring many different systems together in a way that you start to create sub-communities. Obviously, this section has many other features which could be added to it. From the top of my mind I can think of integration in terms of the following features that might make some interesting additions to the group section:
Messaging
You could create a "send to group" WYSIWYG section that sends messages to all the group members, the group's administrators, and/or the group owner.
Additionally, you could integrate all the groups that a user is a member of into the messaging system so that the group name could be used as a contact name to blast messages directly from the mail section.
To expand on the last bullet, you could also show all the group members as a separate section of their contacts area.
Friends
Group members can be integrated easily as friends.
Not only you can specify public, private, friends' areas in your user...