Hi Joyce,
Here's my twopenneth, although my own research is less about groups per se and more about organizational culture, but some ideas that crossed my mind:
Gareth Morgan - Images of Organization (various editions) is one of the 'standard texts' in organization theory - it basically sets out various metaphors for understanding organizations (organization as machine, as brain, as organism etc) - might be a good starting point for thinking about how your groups relate to one another.
I have actually read Payne and Cooper (eds) Groups At Work. 1981, Wiley. which seems more directly relevant to your problem, and while i was searching for it in the library catalogue I came across another book called Groups at Work by Marlene Turner (1999).
Another quite famous text is Deal and Kennedy's (2000) Corporate Cultures, which argues not so much for different groups as different 'types' of organization member - people who conform, people who are mavericks etc. Very readable book although it borders on 'popular' sociology rather than an academic text. (Probably why it's so readable!)
Alternatively there are lots of textbooks called 'Organization theory' which are a decent starting point - anything by Mary Hatch is good.