  We give here the exact maximal subgroup growth of two classes of polycyclic
groups. Let $G_k = \langle x_1, x_2, ..., x_k \mid x_ix_jx_i^{-1}x_j \text{ for
all } i < j \rangle$. So $G_k = \mathbb{Z} \rtimes (\mathbb{Z} \rtimes
(\mathbb{Z} \rtimes ... \rtimes \mathbb{Z})$. Then for all $k \geq 2$, we
calculate $m_n(G_k)$, the number of maximal subgroups of $G_k$ of index $n$,
exactly. Also, for infinitely many groups $H_k$ of the form $\mathbb{Z}^2
\rtimes G_2$, we calculate $m_n(H_k)$ exactly.
