Embedding Group as a Normal Subgroup

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Hi, let G be any group . Is there a way of embedding G in some other
group H so that G is normal in H, _other_ than by using the embedding:

G -->G x G' , for some group G'?

I assume this is easier if G is Abelian and is embedded in an
Abelian group. Is there a way of doing this in general?

Thanks.
 
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