The intersection density conjecture for twice a prime

Let ${\cal I}_n$ be the set of intersection densities of transitive permutation groups of degree $n$, and let $I(n)$ be the maximum value in ${\cal I}_n$. The intersection density conjecture for twice a prime. If $n=2p$ where $p$ is a prime, then

$$I(n)=2.$$

This conjecture is settled in the source, so the case of degrees twice a prime is no longer open.