What do you call someone or a group of people who split off from a main group?

Anything that is a synonym of faction:

band, bloc, bunch, cabal, camp, caucus, cell, circle, clan, clique, club, coalition, combination, combine, combo, concern, conclave, confederacy, conspiracy, contingent, coterie, crew, crowd, design, division, entente, gang, guild, insiders, intrigue, junta, knot, lobby, machine, minority, mob, network, offshoot, outfit, partnership, party, pressure group, ring, schism, sect, section, sector, set, side, splinter group, team, unit, wing.

Thesaurus.com

Schismatic, as defined here

A schismatic is a person who creates or incites schism in an organization or who is a member of a splinter group.

schism is defined here as

a split or division between strongly opposed sections or parties, caused by differences in opinion or belief

For example: A small group split off from the hiking club; these schismatics were determined on multi-day hikes above timberline. The rest of the hiking club wanted easy, one-day hikes, followed by beer in the shade.

Note that a schism is caused by a strong difference about what to do or about what is true, good or right. You don't become a schismatic because you prefer to meet on Thursdays instead of Tuesdays or have some other minor disagreement.

A minority group that is in opposition to the majority (of the same party) is normally referred to as a faction:

faction:

a group or clique within a larger group, party, government, organization, or the like

faction

The following might be used alone or as adjectives with the previous suggestions:

• progressives - [Those] Favoring or promoting change or innovation
• rebels - A person (persons) who rises in opposition ... against an established government
• revolutionaries - A person (persons) who works for or engages in political revolution
• mavericks - An unorthodox or independent-minded person(s)