The order of the departments in the directory widget is chosen based on the sort order given to a department in Core. To adjust the sort order:
  1. Go to Academics
  2. Select Scheduling > Requests and Schedules > Departments & Courses
  3. Click the pencil icon to edit a department
  4. Adjust the sort order to match what you would like the display to be in the front-end directory
  5. Click Save & Close