1. The problem statement, all variables and given/known data Let H be a subgroup of K and K be a subgroup of G. Prove that |G|=|G:K||K|. Do not assume that G is finite 2. Relevant equations |G|=|G/H|, the order of the quotient group of H in G. This is the number of left cosets of H in G. 3. The attempt at a solution I would use LaGrange's Thm, but G is not necessarily finite. I thought a good idea would be to try to find an isomorphism from G/K x K/H to G/H. I defined A(aK x bH)=abH, but I am having trouble proving it is an isomorphism (not even sure it is one!). Is this the right approach? If not, what would be a better way?