Let G={1, 7, 17, 23, 49, 55, 65, 71} under multiplication modulo 96. Express G as an external and an internal direct product of cyclic groups.

I know that lGl =8, so G is isomorphic to either Z8, or G is isomorphic to the external direct product of Z4 Z2, or G is isomorphic to the external direct product of Z2 Z2 Z2. But I'm not sure what to do next.