The normalizer conjecture for $d52f$-submaximal subgroups

Let $G$ be a finite group, let $A\trianglelefteq G$, and let $H$ be an $d52f$-submaximal subgroup of $G$. The normalizer conjecture. Then $H$ is $d52f$-submaximal in the normalizer $N_G(H\cap A)$. This conjecture concerns the behavior of $d52f$-submaximal subgroups under intersection with normal subgroups and passage to the corresponding normalizer; the source introduces it alongside the homomorphism conjecture as a central problem.