The Collaborative International Dictionary of English v.0.48:

Sodality \So*dal"i*ty\, n.; pl. Sodalities. [L. sodalitas, fr.
   sodalis a comrade.]
   1. A fellowship or fraternity; a brotherhood.
      [1913 Webster]

   2. (R. C. Ch.) Specifically, a lay association for devotion
      or for charitable purposes.
      [1913 Webster]