  In this paper, it is proved that the group generated by Bass units contains a
subgroup of finite index in the group of central units
$\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ of the integral group ring
$\mathbb{Z}G$ for a subgroup closed monomial group $G$ with the property that
every cyclic subgroup of order not a divisor of $4$ or $6$ is subnormal in $G$.
If $G$ is a generalized strongly monomial group, then it is shown that the
group generated by generalized Bass units contains a subgroup of finite index
in $\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$. Furthermore, for a generalized
strongly monomial group $G$, the rank of
$\mathcal{Z}(\mathcal{U}(\mathbb{Z}G))$ is determined. The formula so obtained
is in terms of generalized strong Shoda pairs of $G$.
