Magneto-intersubband oscillations in two dimensional systems with energy spectrum split due to spin-orbit interaction

In the present paper we study magneto-intersubband oscillations (MISO) in HgTe/Hg$_{1-x}$Cd$_x$Te single quantum well with "inverted" and "normal" spectra and in conventional In$_{1-x}$Ga$_x$As/In$_{1-y}$Al$_y$As quantum wells with normal band ordering. For all the cases when two branches of the spectrum arise due to spin-orbit splitting, the mutual arrangement of the antinodes of the Shubnikov-de Haas oscillations and the maxima of MISO occurs opposite to that observed in double quantum wells and in wide quantum wells with two subbands occupied and does not agree with the theoretical predictions. A "toy" model is supposed that explain qualitatively this unusual result.