There are exactly 8 isometries $F$ with $F(l_{1})=l_{2}$, $F(l_{2})=l_{3}$, $F(l_{3})=l_{1}$ and $l_{1} \cap l_{2} \cap l_{3} $ is fixed point.

Question

$l_{1}, l_{2}, l_{3} $ are 3 pairwise orthogonal lines in $\mathbb{E_3}$

Prove that there are exactly 8 isometries $F$ with $F(l_{1})=l_{2}$, $F(l_{2})=l_{3}$, $F(l_{3})=l_{1}$ and $l_{1} \cap l_{2} \cap l_{3} $ is a fixed point.

I have no idea how to prove it. Any hints?