Kiwi,
The JFBCFan module uses Facebook's "Like-Box" widget and that can only be used with Pages. Frankly, Facebook doesn't have a lot of support for Groups from external sites simply because a group is generally supposed to be a 'closed' area to guests. Pages are meant for promotion and open to the public, but Groups are supposed to be invite only and only for select people.. therefore, aren't normally advertised outside of Facebook.
JFBConnect has no support for Groups. About 1.5 years ago, Facebook actually started transitioning most Groups to Pages. They didn't hit all groups, as some were following the ideas I mentioned above (closed, non-promotional type areas), but most were forcibly moved to Pages since they were used more for promotion.
Hope that helps explain. Since there aren't any widgets to pull the feed in automatically, it'd likely have to be some custom code to do so, and we haven't ever done anything with groups. Additionally, on your site, would you want your private Group feed shown? If so, are you sure you don't want a Fan page?
Alex
Groups integration
