I am curious about how the Heegaard genus changes after a finite covering.

Is there anyone constructing an closed hyperbolic 3-manifold $N$ such that

the Heegaard genus of a finite covering of $N$ is less than the Heegaard genus of $N$?

Thank you!

Note: Heegaard genus of a 3-manifold means the minimal genus of all Heegaard splittings.