In 2003, Ge posted a problem list on von Neumann algebras. Question 2 (consisting of three parts) from this list is about the existence of certain maximal subfactors. In this talk, I will explain solutions to this Question. Central to these solutions is the use of maximal subgroups with infinite index in certain ambient groups. We also observe that for any faithful 4-transitive action of a group $G$ on an infinite set, the stabilizer subgroup of any point generates a maximal von Neumann subalgebra of $L(G)$. Combining with known works on constructing faithful highly transitive actions, this gives us many maximal von Neumann subalgebras arising from maximal subgroups. Part of the talk is based on joint work with Adam Skalski.