In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1)\cap H_2\neq 1$ or $St_{G}(H_2)\cap H_1\neq 1$. Its planarity is discussed whenever $G$ is an abelian group. $p$-group. https://www.ealisboa.com/quick-save-Pentair-Female-to-Female-Hose-Adapter-4-For-Sectional-Hose-K21241B-top-mega/