The genus of the subgroup graph of a finite group

For a finite group $G$ denote by $\gamma (L(G))$ the genus of the subgroup graph of $G\mathrm{.}$ We prove that $\gamma (L(G))$ tends to infinity as either the rank of $G$ or the number of prime divisors of $\mathrm{\mid }G\mathrm{\mid }$ tends to infinity.