On connectivity of the prime index graph

‎Let G be a group‎. ‎The prime index graph of $G$‎, ‎denoted by \Pi(G)‎, ‎is an undirected graph whose vertices are all subgroups of G and two distinct comparable subgroups H and K are adjacent if and only if [H:K] or [K:H] is prime‎. ‎In this talk‎, ‎it is shown that if G is a finite group and N is a normal solvable subgroup of G which its order is square free and \Pi(G/N) is connected‎, ‎then Pi(G) is connected‎.