OK, now I'm confused. Is the semiauto Thompson 1927A5 pistol classified as AOW?
It has a vertical foregrip. Just a few minutes ago, I found one advertised on that gun auction site "which cannot be named here".
UPDATE - I think I found the answer - the 1927A5 had a 13 inch barrel, giving it an overall length of 26 inches - supposedly, this overall length made it exempt from AOW status