  We study singularity formation of K\"ahler-Ricci flow on a K\"ahler manifold
that admits a horizontally homothetic conformal submersion into another
K\"ahler manifold. We will derive necessary and sufficient conditions for the
preservation of horizontally homothetic conformal submersion along the flow and
establish the formation of type I singularity together with a standard
splitting of the Cheeger-Gromov limit. This generalizes the setup of Calabi
symmetry that was discussed in \cite{1} and \cite{2}, thus gives new proofs for
the results listed there.
