The Jesuits have authority over matters of heresy, while the Dominicans have authority over areas of moral obedience and there was thusly an overlap during the Inquisition.
The Jesuits also used the Office of Holy Inquisition (which lasted for hundreds of years and wasn’t solely confined to Spain) to advance their power within the Church, to the point where they were denounced as a heretical order.
They now run the Society for the Propogation of the Faith, which is an interesting little outfit all it’s own.
