Nuclear fission is a decay process by which a heavy nucleus splits into two or more lighter nuclei. It plays a crucial role in the synthesis of superheavy elements, the rapid neutron-capture process, nuclear energy application and so on. The fission barrier is an important property of heavy nuclei, because its height and width directly relate to the lifetimes of heavy nuclei, and influence the charge yield, mass yield, and kinetic energies of fission fragments. In our study, the potential energy curves of actinide nuclei are obtained from the relativistic density functional theory in three-dimensional (3D) lattice when the axial symmetry, reflection symmetry and V_4 symmetry are broken in turn. The effects of all the quadrupole and octupole deformation degrees of freedom on the inner barrier, outer barrier, and the fission isomeric state are investigated. It is found that breaking the reflection symmetry can lower the outer fission barriers significantly, breaking the axial symmetry can lower both the inner and outer barriers, breaking the V_4 symmetry has little effect on the inner and outer barriers, and the fission isomeric state is almost unaffected by symmetry breaking. Based on the relativistic density functional PC-PK1 and monopole pairing interaction, our results well reproduce the empirical values of the inner and outer barriers extracted from experiments, and the energies of the fission isomeric states are slightly underestimated. All the data presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00229.