There is a semi direct product if you go $\theta: Q \rightarrow Aut(H)$.
$H = C_{17}, Q = C_2$.
$Aut(H)\cong C_{16}$.
From here, how do I construct the semi direct products?
I said, in $C_{16}$, there are two elements of order that divide $2$, which are $1$ and $2$. Therefore there are two semi direct products. Also $17 \times 2 = 34$ tells me that in both semi direct products there will be $34$ elements.
How do I construct the semi direct products from here though?