  We present the ground and excited state spectra of singly, doubly and
triply-charmed baryons by using dynamical lattice QCD. A large set of baryonic
operators that respect the symmetries of the lattice and are obtained after
subduction from their continuum analogues are utilized. These operators
transform as irreducible representations of SU(3)$_F$ symmetry for flavour,
SU(4) symmetry for Dirac spins of quarks and O(3) symmetry for orbital angular
momenta. Using novel computational techniques correlation functions of these
operators are generated and the variational method is exploited to extract
excited states. The lattice spectra that we obtain have baryonic states with
well-defined total spins up to 7/2 and the low lying states remarkably resemble
the expectations of quantum numbers from SU(6)$\otimes$O(3) symmetry.
