  We perform extended group analysis for a system of differential equations
modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra
of this system is proved to be infinite-dimensional. We also find the complete
point symmetry group of this system, including discrete symmetries, using the
megaideal-based version of the algebraic method. Optimal lists of one- and
two-dimensional subalgebras of the maximal Lie invariance algebra in question
are constructed and employed for obtaining reductions of the system under
study. Since this system contains a subsystem of two equations that involves
only two of three dependent variables, we also perform group analysis of this
subsystem. The latter can be linearized by a composition of a fiber-preserving
point transformation with a two-dimensional hodograph transformation to the
Klein-Gordon equation. We also employ both the linearization and the
generalized hodograph method for constructing the general solution of the
entire system under study. We find inter alia genuinely generalized symmetries
for this system and present the connection between them and the Lie symmetries
of the subsystem we mentioned earlier. Hydrodynamic conservation laws and their
generalizations are also constructed.
