For the on call system that I ran until recently, there are about a dozen on call teams responsible for parts of the service. Each team has a primary and backup engineer, generally on a 7x24 shift that lasts a week. Most weeks it's not very busy.

Working with them during an incident is an on call comms lead, who handles outside-of-team comms (protecting the engineers), and an engineering lead (who is a consultant, advisor, and can approve certain actions).

For big incidents, an exec incident manager is involved. They primarily help with getting resources from other teams.