In an oligarchy, the banks, universities, media, courts, etc., conspire in a high/low alliance with the poor, against the middle, to oppress the middle class.
In a monarchy, the King conspires in a high/low alliance with the low, against the middle, to oppress the middle. The middle is Goldman Sachs, Harvard, NY Times, the courts, etc. The low is combines both the middle class and poor.
Oligarchy is left-wing and monarchy is right-wing.