Is it possible to create sub-folders under a "Group" in Documents?

I have an organization with a group set up to share documents.

Is it possible to create sub-folders under that group? When I try to create a new folder, it just creates it under my own folders instead of under the group.

Is there a better way to do this?

I have a group of users, a marketing group, that needs to have access to files. these files need to be separated by type.

Should I set it up another way, maybe in a Workspace?

thanks,

Scott