The Automorphism Group of the Leech Lattice modulo a center of order two is called ``the'' Conway group. There are 15 exceptional Conjugacy Classes of the Conway group. This group, combined with the Groups and obtained similarly from the Leech Lattice by stabilization of the 1-D and 2-D sublattices, are collectively called Conway groups. The Conway groups are Sporadic Groups.
See also Leech Lattice, Sporadic Group
References
Wilson, R. A. ``ATLAS of Finite Group Representation.''
http://for.mat.bham.ac.uk/atlas/html/contents.html#spo.