Dirac sextic oscillator in the constant magnetic field

We introduce a Dirac equation which reproduces the usual radial sextic oscillator potential in the non-relativistic limit. We determine its energy spectrum in the presence of the magnetic field. It is shown that the equation is solved in the context of quasi-exactly-solvable problems. The equation possesses hidden sl₂-algebra and the destroyed symmetry of the equation can be recovered for specific values of the magnetic field which leads to exact determination of the eigenvalues.