Our company uses Google Apps for Enterprise.
I know I am a member of several groups, where in the interface can I see which groups I am a member of?
Is there a place I can see all the company groups/mailing lists and who's a member of them?
From the black bar at the top of each page, you should have "Groups".
Select that, then select My Groups.
You can only see all the groups and membership if you are an admin of your domain (company).