  For a finite group $G$, we define the inclusion graph of subgroups of $G$,
denoted by $\mathcal I(G)$, is a graph having all the proper subgroups of $G$
as its vertices and two distinct vertices $H$ and $K$ in $\mathcal I(G)$ are
adjacent if and only if either $H \subset K$ or $K \subset H$. In this paper,
we classify the finite groups whose inclusion graph of subgroups is one of
complete, bipartite, tree, star, path, cycle, disconnected, claw-free. Also we
classify the finite abelian groups whose inclusion graph of subgroups is
planar. For any given finite group, we estimate the clique number, chromatic
number, girth of its inclusion graph of subgroups and for a finite abelian
group, we estimate the diameter of its inclusion graph of subgroups. Among the
other results, we show that some groups can be determined by their inclusion
graph of subgroups
