  The intersection graph of a group $G$ is an undirected graph without loops
and multiple edges defined as follows: the vertex set is the set of all proper
non-trivial subgroups of $G$, and there is an edge between two distinct
vertices $H$ and $K$ if and only if $H\cap K \neq 1$ where $1$ denotes the
trivial subgroup of $G$. In this paper we classify all finite groups whose
intersection graphs are $K_{3,3}$-free.
