On the index system of well-rounded lattices

Let $\text{Lb}$ be a lattice in an $n$-dimensional Euclidean space $E$ and let ${\text{Lb}}^{\mathrm{\prime }}$ be a Minkowskian sublattice of $\text{Lb}$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\text{Lb}$. We consider the set of possible quotients $\text{Lb}\mathrm{/}{\text{Lb}}^{\mathrm{\prime }}$ which may exists in a given dimension or among not too large values of the index $[\text{Lb}:{\text{Lb}}^{\mathrm{\prime }}]$, indeed $[\text{Lb}:{\text{Lb}}^{\mathrm{\prime }}]\le 4$, or dimension $n\le 8$.