Hint: Given any group of order and any , .
In the case of , what does this tell you about the coset ?
Let H be a normal subgroup of finite group G. If the order of the quotient groups is m, prove that is in H for all .
So since H is normal, there are no distinctions between left and right cosets in G.
G is a finite group. Let o(G) = n. The o(G/H) = m.
Don't know where to go after this...