Sparta,
•Athens had a Direct democracy, Aristocracy, Athenian democracy type government.
•Sparta had Oligarchy, Monarchy, Aristocracy, Republic, Diarchy types of government.
ol·i·gar·chyDictionary result for oligarchy
/ˈäləˌɡärkē/Submit
noun
a small group of people having control of a country, organization, or institution.
"the ruling oligarchy of military men around the president"