Duane is right. When I search for "feline", the groups are sorted like:
. . .
. . .
(They all have "feline" in the description.)
That's reverse alphabetical order by lowercase, followed by reverse alphabetical order by uppercase, without regard to group size or history or activity.
Someone could create a group "zzzzzzzzzzz" with a bunch of terms in the description and appear at the top of the search results for each of those terms.
I'm not sure of the limitations of Elasticsearch, but there should be a better way to sort the list, probably by reverse message volume (higher number of messages means higher in the results). Possibly premium groups before basic groups, which would be another perk of premium.