  We describe here the lower garland of some lattices of intermediate subgroups
in linear groups. The results are applied to the case of subgroup lattices in
general and special linear groups over a class of rings, containing the group
of rational points T of a maximal non-split torus in the corresponding
algebraic group. It turns out that these garlands coincide with the interval of
the whole lattice, consisting of subgroups between T and its normalizer.
