  Let $H$ be a locally compact group and $K$ be an LCA group also let
$\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be
the semidirect product of $H$ and $K$ with respect to $\tau$. In this article
we define the Zak transform $\mathcal{Z}_L$ on $L^2(G_\tau)$ with respect to a
$\tau$-invariant uniform lattice $L$ of $K$ and we also show that the Zak
transform satisfies the Plancherel formula. As an application we show that how
these techniques apply for the semidirect product group
$\mathrm{SL}(2,\mathbb{Z})\ltimes_\tau\mathbb{R}^2$ and also the
Weyl-Heisenberg groups.
