Just speaking theoretically, based on a combination of the canonical strength of the Order and your best guesses as to the Order's own limitations and strengths.
This could be any group, but they need to have real power backing them up. Magic Resistance is practically paramount if they are to put up any kind of struggle, given that if a purely mundane group had that kind of power the Code would probably be ignored in favor of preventing the Order's utter destruction (though how mundanes would get that power without the help of another Realm is beyond me).
I suppose a good starting place is to look at the Church. The Order knows that the Church could defeat the Order of Hermes if they went to war, due to the potentially limitless power of God, the powers available to God's servants in the form of Invocation Wonders and other abilities as presented in RoP:D, the great wealth and numbers of churchmen, and the practically guaranteed intervention of a very large number of very powerful Divine creatures on the side of the non-Magi. Of course, that is a bit abstract; God's limitless (as far as anyone can ascertain, at any rate) power, combined with the wide variance of power available to Divine creatures, means that the example of the Church being able to defeat the Order doesn't really provide any useful information on just how much power the Order of Hermes can stand up to.
There are the Rival Magic groups; I've only read the Introduction of that book so far, but presumably, unlike a conglomeration of Gifted Hedge Wizards, if one of those groups got the Parma Magica or an equivalent and enough time to adapt for the social evolution it would bring, they could be roughly equal in power to the Order of Hermes. I'm pretty sure that's the whole point of the divide between that book and Hedge Magic Revised Edition, after all.
Or maybe they couldn't. I mean, having equivalent magical strength might not be enough by itself to match up to the wealth, pre-establishment, versatility, and existence of hundreds of years of developmental knowledge of the Order of Hermes, never mind its relative size compared to other groups.
This question applies to large groups of Supernatural creatures, too, of course. It would take an extremely large amount of power for a single creature to be able to trade blows with the entire Order, as even individual old Magi are extremely powerful, and against a singular opponent that could otherwise destroy the entire Order, the oldest and most powerful Magi are certain to come together and devise an extremely powerful group ritual that could penetrate nearly any amount of Might-based Magic Resistance and have an appropriately powerful effect to stop a creature of nearly any level of power. And that's just trading magic blows; the Order can raise mundane armies and utilize powerful mundane tactics, divert other powerful supernatural creatures against the invader, and would have extreme financial and evasive resilience against being beaten down faster than they can recover, given that they can scatter, teleport, hide their presence, and still keep in fairly good contact with one another while hiding their presence and teleporting and actually physically hiding themselves simultaneously.
It's more feasible with a larger group of less powerful creatures, but then it raises questions. What kind of resources to they need? Food, perhaps wealth of their own, things they need to sustain their own existence in the case of Faeries, resistance against re-banishment to Hell in the case of Infernals? How much raw power of their own might they need? Might, ability versatility? I mean, sure, a large group of Might 30 Faeries marching around breathing storms of ice might leave Spring covenants filled with younger Magi utterly helpless, but any organized resistance on the part of middle-aged Magi or even specialized defensive measures employed against their primary method of attack on the part of those younger Magi could leave them struggling to cause damage; a passing glance by the oldest and most powerful Magi would leave them either destroyed or completely obsolete.
So, yeah. Obviously, the entire strength of the Order may vary from saga to saga, but there are also a large number of assumptions set by the rulebooks, that they follow when giving examples and describing the Order's interaction with things. All strategies are viable, as long as they are relatively secure; whether it takes 50 seconds, 50 days, or 50 years, as long as it effectively defeats, debases, and eradicates the Order of Hermes, though again, it doesn't qualify if the Order can feasibly continue to recover faster than it is brought down for an indefinite length of time, or if it is such a flimsy method of attack that a single Major or lesser Breakthrough in Hermetic theory or a single clever political maneuver would be enough to easily remove the problem. Following the generally assumed power, political influence, and wealth capacity of the Order (or the closest estimate you can make based on your own interpretations of things) in the year 1220, what kinds of resources and power are needed for a creature or group to stand a reasonable chance of defeating and destroying the entire Order of Hermes? What do you guys think?