Can a Facebook group be a fan of a company page?

[Kosmos]

I administer a company's fan page on Facebook, but I can't figure out if a Group can be a fan of someones page. I want to create a new Page as the main point of contact for an education organization, but there are many sub-groups within the organization (ie; classes, teachers, different programs, etc.) If groups cannot become fans of a page, does anyone have any recommendations of how I can integrate groups with a page?

Any help would be greatly appreciated!

Thanks in advance!