  For most (and possibly all) non-associative finite simple Moufang loops,
three generators of order 3 can be chosen so that each two of them generate a
group isomorphic to $(3, 3 | 3, p)$. The subgroup structure of $(3, 3 | 3, p)$
depends on the solvability of a certain quadratic congruence, and it is
described here in terms of generators.
