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As far I can see, actually your groups are bassicaly empty, could you populate couple of groups with some wall posts, photo, videos and then check if the groups will appear in the most active groups?
I'm not aware of any module which may display the "the group" to be honest, maybe you could check on our addonss page.
I followed your guideline already but it still doesn't work. I did couple of different activities, like text status, photos, videos.... in the group and I tried one status with another group but it still doesn't work for me....
It seems that, this problem was fixed for community page since it's working like a charm, but it's still not working for a module. This's why I must consult this matter with our developers.