I just turned in an exam today and I wanted to answer this question, but I couldn't so I had to choose another (you could omit one question).
Up to isomorphism, we had to determine all groups of order 308.
I know that I have to use the Sylow theorems. We can have just one Sylow subgroup of order 11, we can have 1 Sylow subgroup of order 7 or 22 Sylow 7-subgroups, and 1,11,7,or 77 sylow 2-subgroups. I know I need to consider the eight cases and break it down from there, but I don't know how...