Bit rusty. I presume this is D6β with 12 elements, r being a rotation through pi/3, and s a reflection (of some description).
And H is the subgroup generated by the two elements r3,s
Where does your r2 come from?
I've just realised that I was taking r as a rotation by pi/4 instead of pi/3. I'll take a look my working out in the morning and post again if I need help.