  Let $G$ be a group. The prime index graph of $G$, denoted by $\Pi(G)$, is the
graph whose vertex set is the set of all subgroups of $G$ and two distinct
comparable vertices $H$ and $K$ are adjacent if and only if the index of $H$ in
$K$ or the index of $K$ in $H$ is prime. In this paper, it is shown that for
every group $G$, $\Pi(G)$ is bipartite and the girth of $\Pi(G)$ is contained
in the set $\{4,\infty\}$. Also we prove that if $G$ is a finite solvable
group, then $\Pi(G)$ is connected.
