a note on the order graph of a group

The order graph of a group $g$, denoted by $gamma^*(g)$, is a graph whose vertices are subgroups of $g$ and two distinct vertices $h$ and $k$ are adjacent if and only if $|h|big{|}|k|$ or $|k|big{|}|h|$. so $gamma^*(g)$ is the empty graph if and only if $g$ is a prime number. so we only consider the groups whose orders are not prime. this graph has studied in [?]. in this paper, we study the connectivity and diameter of this graph. we show that the order graph of a non-simple group is a connected graph with diameter less than four with only one family exception. also we give a connection between prime graph and order graph.