My take on this is - I mostly agree with Mark's comment from 2014 - "In terms of categorizing groups, that opens a big can of worms. Perhaps instead, we could have group owners themselves create a set of tags for their groups. I'm much more a fan of bottom-up organizational structures than top-down taxonomies. They scale better and, I think, can be more accurate."
And then he asks "What do you think about this?" - so we're still discussing it.
Yahoo has 17 very broad categories - "Business & Finance, Computers & Internet, Cultures & Community, Entertainment & Arts, Family & Home, Games, Government & Politics, Health & Wellness, Hobbies & Crafts, Music, Recreation & Sports, Regional, Religion & Beliefs, Romance & Relationships, Schools & Education, Science, Adult" - the last one of which we can drop.
I would suggest each group have a category from the above list plus a set of tags/keywords to further refine the interests of the group. The category can be used for filtering when searching for a group to set the "playing field" if you will. (search for groups inside Family&Home with the following keywords...)
PS I would resist having an "Other" category as it tends to become a catchall.