Just as a reminder, anyone can have not only one or more free Google calendars (personal/church/ministry) but also you can “subscribe” to other calendars, and see them all on the same screen. Whenever I view my personal Google calendar, I also see all my local church calendar events, plus all district calendar events, at the same time. I can switch any subscribed calendar to visible or invisible easily. The links to subscribe to the district's departmental calendars are right on the calendar page on the district website, just above the calendar. Also present there is a handy link for department leaders to log into Google to edit their department calendar.
On our church website, our Google calendar combines into a single display both our local church events and all district departmental events (just as the district calendar combines all the various departmental calendars into a single view).
Go check it out now: