  We consider the hidden subgroup problem on the semi-direct product of cyclic
groups $\Z_{N}\rtimes\Z_{p}$ with some restriction on $N$ and $p$. By using the
homomorphic properties, we present a class of semi-direct product groups in
which the structures of subgroups can be easily classified. Furthermore, we
show that there exists an efficient quantum algorithm for the hidden subgroup
problem on the class.
