To solve the expression ( 549 \times 308 - \frac{8904}{33 \times 507 - 16647} ), we will break it down step by step.

Calculate ( 549 \times 308 ):
[
549 \times 308 = 169932
]

Calculate ( 33 \times 507 ):
[
33 \times 507 = 16731
]

Calculate ( 33 \times 507 - 16647 ):
[
16731 - 16647 = 84
]

Calculate ( \frac{8904}{84} ):
[
\frac{8904}{84} = 106
]

Now combine the results:
[
169932 - 106 = 169826
]

Thus, the final result is:
[
\boxed{169826}
]