The Collaborative International Dictionary of English v.0.48:

Synarchy \Syn"ar*chy\ (s[i^]n"[.a]r*k[y^]), n. [Gr. synarchi`a,
   fr. syna`rchein to rule jointly with; sy`n with + 'a`rchein
   to rule.]
   Joint rule or sovereignty. [R.] --Stackhouse.
   [1913 Webster]