The question is to work out the number of semi-direct products for from Q to H, where
$ H = C_{42} , Q = C_{3} $
I did:
$Aut(C_{42}) = C_2 \times C_6 = C_{12}$
3 divides 12 telling us that they're are some semidirect products.
If we let Q = (1, 2, 3). We can see that they're are 3 elements in Q (1, 2 and 3) that divide 12, thus there are 3 semi direct products.
Is this correct reasoning?