Hi ~ Mixed up is right. Group therapy for me was run by the psychiatrist. A support group is run by a "chairperson" who usually is a lay person who has the same problem as everyone else but perhaps has more time in the group as everyone else. That's been MY experience.
My Group Therapy was covered by my insurance, and I was inpatient at the time too, so i have no idea how much it cost.
I wish you the very best. Hugs, Lee