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 of $G$ are (this can be checked by GAP):
$M_1=\langle(6,7),(1,2,3,4,5)\rangle$,
$M_2=\langle (2,5)(3,4),(1,2,3,4,5)\rangle$,
$M_3=\langle(2,5)(3,4)(6,7),(1,2,3,4,5)\rangle$,
$M_4=\langle(6,7),(2,5)(3,4)\rangle$,
$M_5=\langle(6,7),(1,4)(2,3)\rangle$,
$M_6=\langle(6,7),(1,2)(3,5)\rangle$,
$M_7=\langle(6,7),(1,5)(2,4)\rangle$, and
$M_8=\langle(6,7),(1,3)(4,5)\rangle$.
Now consider $H_1=\langle(6,7)\rangle$ and $H_2=\langle(1,2,3,4,5)\rangle$.
