  We investigate a stronger formulation of Webb's conjecture on the
contractibilty of the orbit space of the p-subgroup complexes in terms of
finite topological spaces. The original conjecture, which was first proved by
Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated in
terms of the topology of certain finite spaces. We propose a stronger
conjecture, and prove various particular cases by combining fusion theory of
finite groups and homotopy theory of finite spaces.
