  Background: The isoscalar giant monopole resonance (ISGMR) splits into two
peaks in prolately deformed nuclei. When a nucleus is triaxially deformed, a
peak appears in the middle between the two peaks.
  Purpose: We investigate the mechanism of the appearance of the middle peak in
the ISGMR in triaxial nuclei.
  Method: We perform the constrained Skyrme-Hartree-Fock-Bogoliubov (CHFB)
calculation for arbitrary triaxial shapes in $^{100}$Mo. We calculate the
strength functions of the isoscalar monopole (ISM) and IS quadrupole modes on
the CHFB states. Furthermore, we investigate vibrations of matter distributions
in $x$, $y$, and $z$ directions induced by the external ISM field, with the $z$
axis being the longest axis of the triaxial shape.
  Results: The middle peak in the ISM strength evolves from the triaxial degree
$\gamma=0^\circ$ to $60^\circ$. This is because the difference between the
vibration in $x$ direction and that in $y$ direction is evident with an
increase in $\gamma$ and the quadrupole $K=2$ component of the induced density
of the ISM at the middle peak increases as $\gamma$ increases, where $K$
denotes the $z$ component of the angular momentum. This property is also
obtained in the unperturbed ISM strength without the residual fields.
  Conclusions: The mixing between the monopole and quadrupole modes is
primarily determined by the ground-state deformation. Therefore, the ISM
strength of the middle peak becomes strong as the triaxial degree in the ground
state increases.
