A group isomorphic to a subgroup of a direct product of quotient groups

#group_theory

Let $G$ be a finite group and $H, K ⊴ G$ be normal subgroups of relatively prime order. Prove that $G$ is isomorphic to a subgroup of $G / H \times G / K$ .

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Let $G$ be a finite group and $H,K\mathrel{\unlhd}G$ be normal subgroups of relatively prime order. Prove that $G$ is isomorphic to a subgroup of $G/H\times G/K$.