subgroup intersection graph of finite abelian groups

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in this paper‎, ‎we obtain a lower bound for the independence number of subgroup intersection graph‎. ‎we characterize certain classes of subgroup intersection graphs corresponding to finite abelian groups‎. ‎finally‎, ‎we characterize groups whose automorphism group is the same as that of its subgroup intersection graph‎.