Ryba (1988) showed that its triple cover has two 45-dimensional representations over the field with 7 elements, exchanged by an outer automorphism.
Wilson (1985) and Yoshiara (1985) independently found the 13 conjugacy classes of maximal subgroups of O'N as follows: In 2017 John F. R. Duncan, Michael H. Mertens, and Ken Ono proved theorems that establish an analogue of monstrous moonshine for the O'Nan group.
Their results "reveal a role for the O'Nan pariah group as a provider of hidden symmetry to quadratic forms and elliptic curves."
The O'Nan moonshine results "also represent the intersection of moonshine theory with the Langlands program, which, since its inception in the 1960s, has become a driving force for research in number theory, geometry and mathematical physics."
An informal description of these developments was written by Erica Klarreich (2017) in Quanta Magazine.