The groups need separate topics within the group. The link to a forum that can be public, or not, is nice for a different use. People are use to having topics, threads, and sub threads. In the groups as is, there is just a line of comments with no topics. Again we currently have a 1/2 baked system that was never finished. The "Forum Feed" almost does it, but is also 1/2 baked with out a usable way for users to display images.
There are Boonex Market modules that addresses many of the shortcomings of the Group module. Modzzz even wrote a complete replacement module; Advanced Groups.