It is shown that the four quantum trefoil solitons that are described by the irreducible representations D-3/2, of the quantum algebra SLq(2) [and that may be identified with the four families of elementary fermions (e, mu, tau; nu(e)nu(mu)nu(tau); d, s, b; u, c, t)] may be built out of three preons, chosen from two charged preons with charges (1/3, 1/3) and two neutral preons. These preons are fermions and are described by the D-mm(1/2), representation of SLq(2). There are also four bosonic preons described by the D-mm(1), and D-00(0) representaions of SLq(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable.