It seems that there are some examples. Let $G=D_{10}\times S_2$. Then the frattini subgroup of $G$ is trivial and the maximal subgroups are (that can be check by GAP):
$M_1=<(6,7),(1,2,3,4,5)>$, $M_2=<(2,5)(3,4),(1,2,3,4,5)>$, $M_3=<(2,5)(3,4)(6,7),(1,2,3,4,5)>$, $M_4=<(6,7),(2,5)(3,4)>$, $M_5=<(6,7),(1,4)(2,3)>$, $M_6=<(6,7),(1,2)(3,5)>$,
$M_7=<(6,7),(1,5)(2,4)>$, and $M_8=<(6,7),(1,3)(4,5)>$. Now consider $H_1=<(6,7)>$ and $H_2=<(1,2,3,4,5)>$.