AFAIK there are three scenarios;

1) Non-Dispersive medium (eg. vacuum) : v(g) = v(p) = c

2) Normal Dispersion medium (eg. in water) : v(g) < v(p)

3) Anomalous Dispersion medium (eg. absorbing materials) : v(g) > v(p)

where (simplified);

v(g) : group velocity which can be thought of as a function of the overall wave packet (i.e. pulse) and hence contains the actual energy/information/signal.

v(p): phase velocity which can be thought of as a function of a single wave and hence the crest of that wave.