  A satisfactory description of bound and scattering states of the
three-nucleon (3N) system is still lacking, contrary to what happens in the
two-nucleon case. In the framework of chiral effective theory, it is possible
that a realistic 3N interaction will require the inclusion of subleading
contact terms, which are unconstrained by chiral symmetry. We construct the
minimal 3N contact Lagrangian imposing all constraints from the discrete
symmetries, Fierz identities and Poincar\'e covariance, and show that it
consists of 10 independent operators. By integrating out the pions from the
effective theory we derive the pion-induced contributions to the corresponding
low-energy constants (LECs), and find no clear signal of convergence of the
pionful theory between N2LO and N3LO.
