How to prove that a group affords no epimorphism in $S_3$

Question

Good evening,

I want to prove that the group $G = \langle a, d \mid a d a^{-1} d a = d a d^{-1} a d \rangle$ affords no epimorphism in $S_3$ (the group of the permutations of $\{1, 2, 3\}$). I tried many frequent tools to prove that groups afford no morphism (orders of elements, etc...), but it didn't work.

How may I proceed?

Thank you very much,

Respectfully,

AF