Hopf-Galois Structures of Squarefree Degree

Let $n$ be a squarefree natural number, and let $G$, $\mathrm{\Gamma }$ be two groups of order $n$. We determine the number of Hopf-Galois structures of type $G$ admitted by a Galois extension of fields with Galois group isomorphic to $\mathrm{\Gamma }$. We give some examples, including a full treatment of the case where $n$ is the product of three primes.