High spin states of Dy-144 have been studied through in-beam gamma-ray spectroscopy by using the reaction Mo-92(Fe-56,2p2n). It has been found that the continuation of the ground-state band forks into three Delta I=2 bands above the 8(+) state. This forking has been attributed to the alignments of pi h(11/2)(2) or nu h(11/2)(-2) configurations with the help of the systematics in neighboring nuclei. Additionally a negative-parity sideband of Delta I=2 cascades has been observed to start from the 5((-)) state and continue to a dipole band above the (13(-)) state through another negative-parity sideband of Delta I=2 cascades in between. These structures have been discussed from the viewpoint of a competition between "Magnetic Rotation" and "Anti-magnetic Rotation" based on a classical particles-plus-rotor model.</p>.