in which type of dictatorship does a small group of individuals exercise complete control over a countrys government?

the answer is an oligarchy

Oligarchy

Explanation:

This word refers to a type of government in which few people rule. They often use despotic power to do so, this means, the exercise of absolute power using oppression and cruelty. An oligarchy can operate disguised as a democracy as few people use their influence to change things.

This way of maintaining power is related with a dictatorship in which a single person or a small group of persons rule without constitutional limitations.

As you can see, an oligarchy can or can not be a dictatorship, it depends on the methods it uses to maintain power.