Comparing them to the Inquisition and the Holy Brotherhood (Santa Hermandad) isn't too far off the mark.

But it's the Papal Inquisition, not the Spanish Inquisition, that is a suitable model. The Papal Inquisition was formed for the purpose of suppressing heretics, which the Order of the Inquisition and Order of Doctrine and Ordination are responsible for. (The Spanish Inquisition was formed for the purpose of finding out false converts among the Jews and Moors who remained in Spain after the Reconquista. You have to study Spanish history to understand why this was considered important.)

@Dogsbody- Completely misunderstood you, I think..