The origin of the g-factor of the two-dimensional (2D) electrons and holes moving in the periodic crystal lattice potential with the perpendicular magnetic and electric fields is discussed. The Pauli equation describing the Landau quantization accompanied by the Rashba spin-orbit coupling (RSOC) and Zeeman splitting (ZS) for 2D heavy holes with nonparabolic dispersion law is solved exactly. The solutions have the form of the pairs of the Landau quantization levels due to the spinor-type wave functions. The energy levels depend on amplitudes of the magnetic and electric fields, on the g-factor gh , and on the parameter of nonparabolicity C . The dependences of two energy levels in any pair on the Zeeman parameter 4 0 h h h Z g m m , where mh is the hole effective mass, are nonmonotonous and without intersections. The smallest distance between them at C 0 takes place at the value Zh n / 2 , where n is the order of the chirality terms determined by the RSOC and is the same for any quantum number of the Landau quantization. The main behavior of the pair of Landau quantization energy levels, for example, of the pair E3 , during the increase of the g-factor gh or equivalently of the Zeeman parameter Zh proportional to it, when these variables change from negative to positive values consists in the approach of two branches up till a minimal separation on the energy scale followed by their further repel and increasing separation between them. For the parabolic bands the maximal approaches takes place at the value n/2 of the dimensionless parameter Zh , where n coincides with the order of the chirality terms introduced into the Hamiltonian by the RSOC. The increasing of the parameter C of the nonparabolicity as well as of the amplitude of the applied perpendicular to the layer electric field increases the separation between the branches.