  It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives
can be constructed by applying the method of nonlinear realizations to the
finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and
SU(1,1|2), respectively. In this work, a similar scheme is realised for
OSp(3|2). It is shown that the N=3 case exhibits a surprisingly richer
structure of invariants, the N=3 super-Schwarzian being a particular member. We
suggest that the extra invariants may prove useful in building an N=3
supersymmetric extension of the Sachdev-Ye-Kitaev model.
