Question inspired by recent events in ROK. It seems to be the holy grail of crazy conspiracy theories that actually happened, involving masons, secret services, and the top echelons of society. I do wonder though whether P2 was more of a really dodgy networking club, or whether it actually came close to running Italy behind the scenes.
It was a front (and really not Masonic in any way, which is why they were kicked out of the Fraternity) for a group of influence peddlers. The Italian government is certainly no stranger to corruption, so it would be over-reaching to say that they were on the verge of "capturing the Italian state," but it certainly was a strong group whose power only waned partially when the scandal broke.