  The nucleus $^{44}$Ti has low-lying levels of various kinds of mutually very
different nuclear structure displaying the richness of the nuclear many-body
dynamics. It is shown that the deformed-basis antisymmetrized molecular
dynamics by the use of the Gogny D1S force reproduces successfully and
unifiedly two types of coexistence phenomena in $^{44}$Ti. Namely, on one hand,
the coexistence of the mean field structure and the cluster structure is
confirmed by verifying the normally deformed structure of the $K^\pi$=$3^-_1$
band with a 1-particle-jump intrinsic configuration and the $\alpha + ^{40}$Ca
cluster structure of the $K^\pi$=$0^-_2$ band. The mixed character of the
mean-field-like structure and the $\alpha + ^{40}$Ca cluster structure of the
ground band is also shown. On the other hand, the coexistence of the normal
deformed mean field and the superdeformed mean field is confirmed by verifying
the triaxial superdeformation of the $K^\pi$=$0_2^+$ band and the
$K^\pi$=$2^+_1$ band which has a 4-particle-jump intrinsic configuration. Good
reproduction of the experimental data is shown for many kinds of quantities
including the energy spectra, electric transition rates, alpha spectroscopic
factors. Preliminary discussions are given on the existence of hyperdeformed
excited states, the relation between superdeformation and clustering and so on.
