Question essentially in the title.
I know that if $ K \subseteq L $ is a finite extension, then $L/K$ is Galois if and only if the fixed field of $ \mbox{Aut}(L/K)$ is $K$.
But is it possible for there to be a finite subgroup $G < \mbox{Aut}(L/K)$ that also has $K$ as a fixed field?
Thanks