The fluctuating part of the total photoionization cross sections up to the 20th single ionization threshold from the ground state of helium are investigated within a planar model of the atom. The calculated fluctuations reproduce existing experimental observations rather well. The fluctuations are mainly due to a dominant series of resonances which can be associated with an approximate quantum number $F=N\ensuremath{-}K$. As the energy approaches the double ionization threshold, the dominant role of a single series as sole contributor is apparently lost as new series start to contribute significantly to the cross sections.