  Composite quantum systems can be in generic states characterized not only by
entanglement, but also by more general quantum correlations. The interplay
between these two signatures of nonclassicality is still not completely
understood. In this work we investigate this issue focusing on computable and
observable measures of such correlations: entanglement is quantified by the
negativity N, while general quantum correlations are measured by the
(normalized) geometric quantum discord D_G. For two-qubit systems, we find that
the geometric discord reduces to the squared negativity on pure states, while
the relationship $D_G \geq N^2$ holds for arbitrary mixed states. The latter
result is rigorously extended to pure, Werner and isotropic states of two-qudit
systems for arbitrary d, and numerical evidence of its validity for arbitrary
states of a qubit and a qutrit is provided as well. Our results establish an
interesting hierarchy, that we conjecture to be universal, between two relevant
and experimentally friendly nonclassicality indicators. This ties in with the
intuition that general quantum correlations should at least contain and in
general exceed entanglement on mixed states of composite quantum systems.
