  Correlations between the harmonic flow coefficients $v_1$, $v_2$, $v_3$ and
$v_4$ of nucleons in semi-peripheral Au+Au collisions at a beam energy of
1.23~AGeV are investigated within the hadronic transport approach
Ultra-relativistic Quantum Molecular Dynamics (UrQMD). In contrast to
ultra-relativistic collision energies (where the flow coefficients are
evaluated with respect to the respective event plane), we predict strong
correlations between the flow harmonics with respect to the reaction plane.
Based on an event-by-event selection of the midrapidity final state elliptic
flow of protons we show that as a function of rapidity, I) the sign of the
triangular flow changes, II) that the shape of $v_4$ changes from convex to
concave, and III) that $v_3\propto v_1v_2$ and $v_4\propto v_2^2$ for all
different event classes, indicating strong correlations between all
investigated harmonic flow coefficients.
