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Let $K/F$ be a finite Galois extension of fields with $Gal(K/F)=\Gamma$. Inan earlier work of Timothy Kohl, the author enumerated dihedral Hopf-Galoisstructures acting on dihedral extensions. Dihedral group is one particularexample of semidirect product of $\mathbb{Z}_n$ and $\mathbb{Z}_2$. In thisarticle we count the number of Hopf-Galois structures with Galois group$\Gamma$ of type $G$, where $\Gamma,G$ are groups of the form$\mathbb{Z}_N\rtimes_\phi\mathbb{Z}_2$ when $N$ is odd with radical of $N$being a Burnside number. As an application we also find the correspondingnumber of skew braces.

On $\mathbb{Z}_N\rtimes\mathbb{Z}_2$-Hopf-Galois structures