Presently there are about 1500 groups? (~30 pages x 50/page). That seems silly but it's a given; the vast majority have ~20 or fewer members. The only sort available is - none - by default they are ordered by number of members. If you know a keyword to search on you can do that
One group is described as "only for asians". Maybe there's one that's only for anti-semites; who's to know but one can search. More generally a user might want to look for broader interest categories of interest; e.g., Atheist, Buddhist, Christian, Hate, Emotional Support, Personal, or even Go-Related things such as Lessons, Beginner, Intermediate, Advanced, Expert and so forth.
A bit of work would be needed to set up categories, probably starting with a review of the existing set.
Presently the only information collected when a Group is created is Group Name, Open to the public (Y or N), Hide details from non-members (Y or N).
Suggest that category choices be available for a group to choose from to describe/advertise itself. In addition, a limited number of freeform keywords could entered.
It is unclear whether the search supports any sort of boolean operations.