Given a finite non abelian group $G$, and it's permutation group $Perm(G)$ how would I go about finding all of the regular subgroups $N$ of $Perm(G)$?
I'm looking at applying the theorem of Greither and Pareigis in Hopf-Galois theory, which states that given a Galois extension $L/K$, with Galois group $G$, there is a bijection between the regular subgroups of $Perm(G)$ normalised by the left regular representation $\lambda$ and the $K$-Hopf Galois structures on $L/K$.
Once the regular subgroups are found, is it then just a case of checking which of these are normalised by $\lambda$ or is there a trick to speed things up a bit?
For example, if $G=\cal{Q}_8$, the group of quaternions, I have seen a paper (http://nyjm.albany.edu/j/2019/25-13v.pdf) that states that there are a certain number of such groups $N$, and it then goes on to explicitly calculate what each group looks like and shows it is regular. The paper doesn't make mention of why this list is exhaustive and how one would go about finding these subgroups in the first place.
I understand that it is a non-trivial undertaking, but I was hoping that there is some tactical approach instead of sheer brute force calculations in each case.