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