The cross section for a neutron-deuteron (nd) radiative capture is calculated using the pionless effective field theory including isospin symmetry breaking (ISB) corrections up to higher order. The triton is studied as a three-body bound state and one has to take into account various ISB effects, relativistic corrections and external electromagnetic currents. The isospin violation in nd radiative capture is improved compared to the one at NLO and N2LO. The cross section is determined to be σtot = [0.505 ± 0.003] mb up to N2LO. A satisfactory agreement between theory and experiment for the calculated cross section has been found by insertion of three-body forces and ISB effects.