Laterally rotating your thighs at the hip joint, the deep external rotators, otherwise known as the ‘deep six’, are a set of six muscles located beneath the gluteus maximus. In no particular order, they are Quadratus Femoris, Inferior Gemellus, Superior Gemellus, Obturator Internus, Obturator Externus, and Piriformis. The inferior and superior gemellus are both long and thin, and originate on the ischium. The Piriformis meanwhile originates on the both the sacrum’s forward surface, and the ilium’s gluteal surface. The two Obturators on the other hand originate along the surface of the obturator membrane, the foramen, and the bones of that region. And finally, the quadratus femoris is rectangular in shape and quite strong, originating on the ischial tuberosity.
The deep external rotators main purpose is laterally rotating the hip joint. To some degree, they also help with adduction and extension.