  The electronic structure of WTe$_2$ and orthorhombic $\gamma-$MoTe$_2$, are
claimed to contain pairs of Weyl type-II points. A series of ARPES experiments
claim a broad agreement with these predictions. We synthesized single-crystals
of MoTe$_2$ through a Te flux method to validate these predictions through
measurements of its bulk Fermi surface (FS) \emph{via} quantum oscillatory
phenomena. We find that the superconducting transition temperature of
$\gamma-$MoTe$_2$ depends on disorder as quantified by the ratio between the
room- and low-temperature resistivities, suggesting the possibility of an
unconventional superconducting pairing symmetry. Similarly to WTe$_2$, the
magnetoresistivity of $\gamma-$MoTe$_2$ does not saturate at high magnetic
fields and can easily surpass $10^{6}$ \%. Remarkably, the analysis of the de
Haas-van Alphen (dHvA) signal superimposed onto the magnetic torque, indicates
that the geometry of its FS is markedly distinct from the calculated one. The
dHvA signal also reveals that the FS is affected by the Zeeman-effect
precluding the extraction of the Berry-phase. A direct comparison between the
previous ARPES studies and density-functional-theory (DFT) calculations reveals
a disagreement in the position of the valence bands relative to the Fermi level
$\varepsilon_F$. Here, we show that a shift of the DFT valence bands relative
to $\varepsilon_F$, in order to match the ARPES observations, and of the DFT
electron bands to explain some of the observed dHvA frequencies, leads to a
good agreement between the calculations and the angular dependence of the FS
cross-sectional areas observed experimentally. However, this relative
displacement between electron- and hole-bands eliminates their crossings and,
therefore, the Weyl type-II points predicted for $\gamma-$MoTe$_2$.
