In this paper, we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial p-group. We prove that the universal cover of its nerve is homotopy equivalent to a wedge of r-spheres where 2r ≥ 4 is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles as introduced in 2.