Is <(12)> a Maximal Subgroup of S_{3}?

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moont14263
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If G is a finite group and M is a maximal subgroup, H is a subgroup of G not contained in M. Then G=HM.

Is this true?
 
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S_{3}, <(12)> maximal, <(23)>, S_{3} not equal <(12)><(23)>
Thank you very much.
 

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