A very basic question that seems to be unsolved: is the class of sofic/hyperlinear groups closed under semi-direct product?

In case of sofic groups the following restricted version is well-known: if $N$ is sofic and $H$ is amenable, then any semidirect product $N\rtimes H$ turns out to be sofic. Is the analogue true for hyperlinear $N$'s?

Thanks in advance for any comment,

Valerio