Groups of people who join together to gain political support for their views are known as

Political parties

Groups of people who join together to gain political supports for their views are known as political parties.

Explanation:

Political parties are group of people who come together in order to exercise power in the government of a nation. These groups of people have the same notion, goals, interests and concerns of how a nation is to be governed. They have laid down political agendas and policies they will work with when they get into power. Thus, their aim is to contest in an election, win and exercise political power.