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Where can I find these two result? And how to charicterize $Z_2$-extension of an Abelian group? If not, can we conunt the number of $Z_2$-extension of an Abelian group? Thank you for your help!

Jian-Bing Liu
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    So I assume you have already classified groups of order $p^3$ and $p^4$? – Hagen von Eitzen Sep 21 '15 at 06:30
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    See this answer to a link classifying groups of order $p^3$. A group of order $2p^3$ is a semi-direct product of its unique Sylow $p$-subgroup and $C_2$, so you need to classify the automorphisms of order at most two as well. – Jyrki Lahtonen Sep 21 '15 at 06:35
  • Thank you for your answer. In fact, I want to know how to count the total number of $Z_2$-extension of an abelian group. Is there some result? Or do you know how to proof? – Jian-Bing Liu Sep 24 '15 at 07:54

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