  We prove existence and compute the limiting distribution of the image of
rank-$\left(d-1\right)$ primitive subgroups of $\mathbb{Z}^{d}$ of large
covolume in the space $X_{d-1,d}$ of homothety classes of
rank-$\left(d-1\right)$ discrete subgroups of $\mathbb{R}^{d}$. This extends a
theorem of Aka, Einsiedler and Shapira.
