Rewrite custom post type permalink to include subdirectory

Hi,
I am creating an add-on that will display conference activities. I’ve setup a custom post type to serve as the activities. The problem I’m encountering is that the single post for each of these item displays as http://site.com/post_type/post_title by default. However, I would like the conference items to be displayed under a page/subdirectory like so http://site.com/conference/post_type/post_title.

I’ve tried setting the rewrite property to conference/post_type in the custom post type registration and the permalink on the edit page looks fine, but when I browse to the link I get a 404.

Is it possible to make the custom post types appear behind a page/subdirectory?