Let G be a finite group which is not isomorphic with any cyclic p-group (p is a prime). We introduce the join graph of subgroups of G. The vertex set of the join graph is the set of all proper subgroups of $G$ which are not contained in the Frattini ubgroup and two vertices H and K are adjacent if and only if H, K =G. We show that the join graph is connected and its diameter is at most 3. The clique number and the chromatic number of the join graph are equal to the number of maximal subgroups of $G$. If the independence number of the graph is at most 7, then G is solvable. Also we ltr"
