  We study electron-positron annihilations into six jets at the parton level in
perturbative Quantum Chromo-Dynamics (QCD), via the elementary processes
$e^+e^-\ar q\bar q gggg$, $e^+e^-\ar q\bar q q'\bar q' gg$ and $e^+e^-\ar q\bar
q q'\bar q' q''\bar q''$, for massive quarks $q, q'$ and $q''$ and massless
gluons $g$. Several numerical results of phenomenological relevance are given,
at three different collider energies and for a representative selection of jet
clustering algorithms. We also present helicity amplitudes and colour factors
needed for the tree-level calculation
