SELECT group_id
FROM group_user
WHERE user_id IN (9,7,6)
GROUP BY group_id
HAVING count(DISTINCT user_id) = 3
AND count(DISTINCT group_id) = 1
makes sure that all 3 ids are in the same group_id and that they're not in any other group.
http://sqlfiddle.com/#!9/540f96/2