Hagiarchy

from The Collaborative International Dictionary of English v.0.48

Hagiarchy \Ha"gi*ar`chy\ (h[=a]"j[i^]*[aum]r`k[y^]), n. [Gr.
   "a`gios sacred, holy + -archy.]
   A sacred government; government by holy orders of men.
   --Southey.
   [1913 Webster]