group theory stumper

The problem is the following: "Let G be a finite group, K a normal
subgrp, and H a subgrp s.t. |K| and |G|/|H| are mutually prime. Show K
a subgrp of H."

It seems like the trick should be to show something like |HK|/|K|, or
|K|/|H cap K|, divides both |K| and |G|/|H|, so that one can conclude
there's only one coset and it must be the trivial one.. But this is
much easier said than done and after spending quite a large time on it
no progress is made. An obvious isomorphism theorem applies, but
doesnt actually end up really helping. Any hints would be appreciated.
The problem is homework.

.

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