  In this paper, the Lie group $G_{NC}^{\alpha,\beta,\gamma}$, of which the
kinematical symmetry group $G_{NC}$ of noncommutative quantum mechanics (NCQM)
is a special case due to fixed nonzero $\alpha$, $\beta$ and $\gamma$, is
three-parameter deformation quantized using the method suggested by Ballesteros
and Musso in "Quantum Algebras as Quantizations of Dual Poisson-Lie Groups" [J.
Phys. A: Math. Theor., 46 (2013), 195203]. A certain family of QUE algebras,
corresponding to $G_{NC}^{\alpha,\beta,\gamma}$ with two of the deformation
parameters approaching zero, is found to be in agreement with the existing
results of the literature on quantum Heisenberg group. Finally, we dualize the
underlying QUE algebra to obtain an expression for the underlying star-product
between smooth functions on $G_{NC}^{\alpha,\beta,\gamma}$.
