on the planarity of a graph related to the join of subgroups of a finite group

‎let $g$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎we define an undirected simple graph $delta(g)$ whose‎ ‎vertices are the proper subgroups of $g$, which are not contained in the‎ ‎frattini subgroup of $g$ and two vertices $h$ and $k$ are joined by an edge‎ ‎if and only if $g=langle h‎ , ‎krangle$‎. ‎in this paper we classify finite groups with planar graph‎. ‎%for this‎, ‎by kuratowski's theorem‎, ‎we have to study subdivisions‎ ‎%of the kuratowski graphs $k_{3‎ , ‎3}$ and $k_5$ in the graph $delta(g)$‎. ‎our result shows that only few groups have planar graphs‎.