You need to check out Shadows of Europe and Loose Alliances. 
That!
Also a peak into
Threats 2 wont hurt.
SoE has a list of the most important Orders and their role. To name just the one that where mentioned here before:
New Jesuits - the fellas first described in Aztlan SB. Basically Vatican Intelligence Service (although they put it more nicely). They like cyber and distrust magic.
Silvestrians - Has the majority of the cathlic church´s mages in it. They are the ones that have a reputation for exorcism & fighting shedim, however, they do lots of other magic tasks as well. It´s also worth mentioning, that IIRC, all (or most) traditional religious burial rites stop from stealing the corps, no magically active person has to be involved AFAIK (i think it was mentioned in
Year of the Comet, where Shedim are described for the first time).
There is also an order or two dedicated to Matrix-related stuff (Augustinians?).
Then There is the
Vigilia Evangelica, which is described in
Loose Aliances - they deal with the really secret library stuff.
Threats 2 describes the New
Order of the Temple Order in detail, which is a secret militant Order of mages and mundanes.
If you are interested in this kind of stuff,
Threats (the 1st) may also be interesting, as it describes the
Black Lodge, a magic society which has some unspoken history with the Vatican and claims to be rooted in the original Knights Templar.