  The W_3 algebra of central charge 6/5 is realized as a subalgebra of the
vertex operator algebra V_{\sqrt{2}A_2} associated with a lattice of type
\sqrt{2}A_2 by using both coset construction and orbifold theory. It is proved
that W_3 is rational. Its irreducible modules are classified and constructed
explicitly. The characters of those irreducible modules are also computed.
