We demonstrate the agreement between the Higgs branches of two N=2 theories
proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory
with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to
the superconformal theory with E_6 flavor symmetry. In mathematical terms, we
demonstrate the equivalence between a hyperkaehler quotient of a linear space
and another hyperkaehler quotient involving the minimal nilpotent orbit of E_6,
modulo the identification of the twistor lines.