Is there a way to create a permanent sidebar in Flutter Web?

I've started building a website using Flutter Web, but have come to the issue of being unable to create a persistent sidebar.

Do you know if there is a way to do so, either by somehow making AppBar vertica; down the side, or by making a permanent drawer, like the one available in MDC Web?

My original idea was to have a Scaffold with this sidebar persisting across Navigator route changes. I tried playing with nested Navigators, but those didn't help me achieve my desired effect.

Thank you very much for your help
--Jakub