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Abstract Algebra

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Order of Intermediate Subgroup

ABSALG-1KX7SY

Suppose $H$ and $K$ are subgroups of a finite group $G$.

If $H\subset K \subset G$, $|H|=36$, and $|G|=504$, what are the possible orders for $|K|$?

A

$36, 72, 252, 504$

B

$36, 72, 504$

C

$36, 252, 504$

D

$36, 72, 144, 216, 252, 504$

E

None of the above.