Phi Mu Alpha Sinfonia's national headquarters, Lyrecrest, is in Indiana but not Indianapolis. It is in Evansville -- it wound up there because a long-time, part-time Executive Director was on the faculty (or administration) at University of Evansville and basically ran the Fraternity out of his office and his home. Then the chance to purchase the house and 13+ acres (which include a pond and an oil well

) which are now Lyrecrest came along. More adjacent land has since been purchased, and new buildings have been bought or built.
I know that a few years back, there was actually an organization of GLO's with HQ's in Indiana.
BTW, did any GLO's HQ, other than Phi Mu Alpha's, sustain any damage in the earthquake that hit Indiana a few months ago. We actually had some major damage -- the floor of the store room, where lots of merchandise waiting to be sold was kept, collapsed. Fortunately, no one was hurt.