  The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice
QCD in the Hamiltonian approach is investigated. As was shown earlier,
${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic
$C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra
constructed from gauge invariant combinations of quark fields. The gluonic
component is isomorphic to a standard CCR algebra over the group manifold
SU(3). The structure of the hadronic part, as presented in terms of a number of
generators and relations, is studied in detail. It is shown that its
irreducible representations are classified by triality. Using this, it is
proved that the hadronic algebra is isomorphic to the commutant of the triality
operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$
(factorized by a certain ideal).
