Does the Jedi Order know about the Order 66 in Star Wars?

The Jedi Order is safe to say that they do know about Order 66 but felt like the Order 66 wouldn't apply to them. All 150 orders would have been presented to the Senate and passed. Debated upon and passed. I doubt the Jedi Order gave it more than a passing thought
I suspect there were no objections to this rule because it sounds perfectly reasonable, if you don't know how it is going to be carried out.

In the event of Jedi officers acting against the interests of the Republic, and after receiving specific orders verified as coming directly from the Supreme Commander (Chancellor), GAR [Grand Army of the Republic] commanders will remove those officers by lethal force, and command of the GAR will revert to the Supreme Commander (Chancellor) until a new command structure is established.

The way it is written, it sounds like a perfectly innocent contingency for in case any Jedi officers go rogue and become a threat to the Republic as a whole. And given that the Sith were clouding their ability of foresight, they had no way of knowing that this order would be given to every GAR commander at once, thus ordering the mass execution of the Jedi. You have to remember, until that very moment, the Jedi trusted the Emperor and believed him to be benevolent.
Order 66 is in the Contingency Orders for the Grand Army of the Republic: Order Initiation, Orders 1 through 150, GAR Document CO(CL) 56-95
But the Jedi Order was no Lawyer or anything, they were fighters busy in a war
And Order 66 is well buried inside of 149…