extremism vs ideology

extremism and ideology both are nouns.

Word	Noun	Adjective	Verb	Adverb
extremism	Yes	No	No	No
ideology	Yes	No	No	No

As nouns, ideology is a hypernym of extremism; that is, ideology is a word with a broader meaning than extremism:

extremism: any political theory favoring immoderate uncompromising policies
ideology: an orientation that characterizes the thinking of a group or nation

Other hypernyms of extremism include political orientation, political theory.

extremism (noun)	ideology (noun)
any political theory favoring immoderate uncompromising policies	an orientation that characterizes the thinking of a group or nation
	imaginary or visionary theorization