Sylow 2-subgroup and Sylow 3-subgroup of $D_{24}$ (of order $48$).

Question

Find Sylow 2-subgroup and Sylow 3-subgroup of $D_{24}$

I have found $n_2 = 1$ or $3$ and $n_3 = 1$ or $4$ or $16$, where $n_2$ & $n_3$ are the number of Sylow $2$-subgroups and Sylow $3$-subgroups respectively, but I am unable to pinpoint the exact solution. I am having difficulty in understanding $D_{24}$ also. Can someone help with this?

Answer 1

Hint: $D_{n}\cong\Bbb Z_n\rtimes\Bbb Z_2$.