Assassin's Creed calls the ancient order opposing the Assassins the Templars.
The Templars are the series' central ideological rivals. They generally seek peace through control and order, while the Assassins defend the freedom of human choice. Their conflict is expressed through the recurring maxim that nothing is true and everything is permitted.
In the fictional chronology, the Templar Order exists across many centuries and often operates through governments, military organizations, corporations, or other institutions. Abstergo Industries is a modern Templar front and becomes especially important in the modern-day storyline.
Several other groups are easy to confuse with the Templars. The Hidden Ones are the early form of the Assassin Brotherhood in Assassin's Creed Origins. The Cult of Kosmos is a separate enemy organization in Assassin's Creed Odyssey. The First Civilization, also called the Isu, predates both factions and created many artifacts central to the series' mythology.