Let $G$ be a finite group and $H$ a subgroup. Let $\mathcal{L}(H \subset G )$ be the lattice of all the intermediate subgroups between $H$ and $G$. **Question:** Can any finite lattice be realized as an intermediate subgroups lattice? *Remark*: It's true for all the finite distributive lattices (see theorem 2.1 [here][1]). [1]: http://www.math.hawaii.edu/~williamdemeo/latticetheory/Palfy-IntervalsInSubgroupLattices-GStA-1993.pdf