It can be extremely difficult to determine the number of groups of order $n$ (upto isomorphism).
Suppose a number $n$ is given and for every proper divisor $d|n$, we know the number of groups of order $d$. Is it then easy to calculate the number of groups of order $n$ (upto isomorphism) that can be expressed as a semidirect product of two or more non-trivial groups ?
According to my calcution with GAP, the groups upto order $59$ , cyclic groups not considered, that are NOT a semidirect product of smaller groups, are :
8 4 Q8
16 9 Q16
32 8 C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)
32 15 C4 . D8 = C4 . (C4 x C2)
32 20 Q32
32 32 (C2 x C2) . (C2 x C2 x C2)
48 28 C2 . S4 = SL(2,3) . C2