1. The problem statement, all variables and given/known data Hey PF, I'm trying to find fields K<M<L such that K:L is Galois but K:M is not. 2. Relevant equations 3. The attempt at a solution My first idea was let K=Q the field of rational numbers and c be a primitive 6th root of unity, so then Q<Q(c^4)<Q(c). Q:Q(c) Is galois, and I'm hoping that Q<Q(c^4) is not. Then again, would c^4 be a third primitive root of unity? If so then Q<Q(c^4) would be Galois I believe. Right? Can anyone help me find something that would work?