How to escalate SLA violation to another group or third party who is not an agent?

While configuring SLA, you would also have to option to set up escalation rules, which would send out notifications to the chosen agents, whenever the configured SLA is violated. This could be set up under Admin > Workflows > SLA Policies > Edit >"What happens when this SLA is violated?" where you could add multiple levels of escalation.

However, only agents(any agent within your Freshdesk Account, even from a different group) in your account could be added under this section and third parties could not be added.