Biblio content, by default, comes sortable by four different categories: Author, Title, Type, Year. So no, out of the box, Biblio does not have a way to do this using it's default filtering tools, but there is almost always a way to get what you want done in Drupal. So let's take a look at one way that we can accomplish this task.
While Biblio does not currently allow for the addition of custom fields, it is very nicely integrated with Taxonomy. If you build a Taxonomy vocabulary listing the departments or groups to be included, then attach the vocabulary to your Biblio content type, your contributors can now tag their Biblio entries with the related department.
A trip into Views will allow you to build a customized display list that you can definitely sort and filter by department.