Separability of Schur rings over an abelian group of order $4p$

An $S$-ring (a Schur ring) is said to be separable with respect to a class of groups $\mathcal K$ if every its algebraic isomorphism to an $S$-ring over a group from $\mathcal K$ is induced by a combinatorial isomorphism. We prove that every Schur ring over an abelian group $G$ of order $4p$, where $p$ is a prime, is separable with respect to the class of abelian groups. This implies that the Weisfeiler–Leman dimension of the class of Cayley graphs over $G$ is at most 2.