Not strange because you misidentified what you were looking for as it's called a golf group or league. The golf club of which you speak is a specific golfing venue that sometimes has a club house(but not all do as some small municipal courses only have a small shop to pay greens fees). Even in high school and college it's known as the golf team.
Now you do have chess clubs, archery clubs, etc. Softball groups are called "teams" and "leagues"(like bowling). Once you have this all figured out...notsocrates(or notplato)you'll have very little trouble finding what you want.
;-)
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