Anarchists wanted the government abolished and to be able to organise for themselves how they should live, without strict rules or laws. This included the CNT, a major anarchist trade union.
Communists:
Communists wanted to create a classless and stateless free society and change privatism to create collective ownership. This included the PCE and POUM (an anti-Stalinist Marxist Party).
Socialists:
Socialists wanted the distribution of wealth equally and corporately owned, with equal opportunity and benefit for all. This included the PSOE, which had links to the UGT trade union and the youth movement FJS.
Republicans/Liberals:
They wanted freedom of speech, democracy, open and fair elections and all citizens to have equal rights. They included Izquierda Republicana and Union Republicana. Mauel Azana was also a Republican.
Conservatives:
Conservatives favoured tradition, wanted to reform society slowly and some wanted to preserve things like religion, others culture. They included CEDA, a Catholic Party formed by Gil Robles.
Monarchists:
Monarchists wanted to restore the monarchy, but just liked the idea of a monarch, not the current monarch. This included Carlists, who wanted an ultra catholic monarchy.
Fascists:
Fascists wanted national unity based on ethnic, cultural, national and radical attributes and is often linked with dictators. This included the Falange, founded by Primo De Rivera's son, and later formed to create Falange Espanola de las JONS.