  We study the degeneracy of quarter BPS dyons in N =4 type II
compactifications of string theory. We find that the genus-two Siegel modular
forms generating the degeneracies of the quarter BPS dyons in the type II
theories can be expressed in terms of the genus-two Siegel modular forms
generating the degeneracies of quarter BPS dyons in the CHL theories and the
heterotic string. This helps us in understanding the algebra structure
underlying the degeneracy of the quarter BPS states. The Conway group, Co_1,
plays a role similar to Mathieu group, M_{24}, in the CHL models with eta
quotients appearing in the place of eta products. We construct BKM Lie
superalgebra structures corresponding to Z_N (for N=2,3,4) orbifolds of the
type II string compactified on a six-torus.
