  The violation of the Svetlichny's inequality (SI) [Phys. Rev. D, 35, 3066
(1987)] is sufficient but not necessary for genuine tripartite nonlocal
correlations. Here we quantify the relationship between tripartite entanglement
and the maximum expectation value of the Svetlichny operator (which is bounded
from above by the inequality) for the two inequivalent subclasses of pure
three-qubit states: the GHZ-class and the W-class. We show that the maximum for
the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838
(1990)] modulo a constant factor, and although it is a function of the three
tangle and the residual concurrence, large number of states don't violate the
inequality. We further show that by design SI is more suitable as a measure of
genuine tripartite nonlocality between the three qubits in the the W-class
states, and the maximum is a certain function of the bipartite entanglement
(the concurrence) of the three reduced states, and only when their certain sum
attains a certain threshold value, they violate the inequality.
