Perhaps, but I belong to groups based on my interests which are completely orthogonal to race: my Church, various interest groups on Facebook, etc.

I work at a small company (c. 600 people), so it isn't big enough to have these kinds of groups, but I'd be more interested in joining a group based on interests, like software development (I do work for a software company), or maybe tabletop gaming. I don't care what race people are, but what their interests are like. Of course, I'm a white guy, so there wouldn't be a white guy group (nor would I want to see one).

And for what it's worth, there are a lot of immigrants at this company, so whites are a minority among mostly Indians and Chinese, etc.