The propagation of internal Alfvén-ácoustic-gravity waves in a compressible, stratified, inviscid, perfectly conducting, isothermal atmosphere in the presence of a horizontal magnetic field is investigated by considering both the horizontal and the vertical component of the group velocity. The vertical component of the group velocity is important because it determines the speed at which energy travels upwards and becomes available for heating the upper regions. The regions of propagation and no propagation of waves are delineated for different magnetic Mach numbers, in a refractive-index domain. The horizontal and vertical group velocities are compared with the corresponding phase velocity of the wave motion. It is found that the horizontal group velocity of the internal waves is always less than the horizontal phase velocity for small magnetic fields and vice versa for large magnetic fields, whereas the vertical group velocity is always opposite in direction to the vertical phase velocity for small magnetic fields and vice versa for large magnetic fields. We have also drawn the reflexion condition in a wave-number-frequency domain for different Mach numbers.