Hopf-Galois structures of isomorphic type on a non-abelian characteristically simple extension

Abstract: Let $L/K$ be a finite Galois extension whose Galois group $G$ is non-abelian and characteristically simple. Using tools from graph theory, we shall give a closed formula for the number of Hopf-Galois structures on $L/K$ with associated group isomorphic to $G$.