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In $D_4\times\mathbb Z_2$, find normal subgroups $H$ of orders $2$,$4$, and $8$. For each $H$ describe $G/H$.

I know what makes a subgroup normal, but I don't know how to find one. And what would it mean to describe G/H? I could think of is maybe the left cosets and isomorphic subgroups?

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    What's $\,D_4\,$ for you? The dihedral group of order $\,8\,$ or the one of order $\,4\,$? Most probably the former, as the later would make things completely trivial.2012-12-14
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    it's the one of order 82012-12-14
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    Is it $D_4 \times \mathbb{Z}_2$ or $D_4 \times \mathbb{Z}_4$? You say both.2012-12-14
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    Note, also, these are not "normal subgroups of $H$", these are "normal subgroups $H$." They are "normal subgroups of" $G=D_4\times \mathbb Z_4$ (or $G=D_4\times \mathbb Z_2$, depending on which you meant.)2012-12-14
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    It's supposed to be D4 x Z22012-12-14

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