Editing Group extension (section)

====Warning====

It may happen that the extensions <math>1\to K\to G\to H\to 1</math> and <math>1\to K\to G^\prime\to H\to 1</math> are inequivalent but ''G'' and ''G''' are isomorphic as groups. For instance, there are <math>8</math> inequivalent extensions of the [[Klein four-group]] by <math>\mathbb{Z}/2\mathbb{Z}</math>,<ref>page no. 830, Dummit, David S., Foote, Richard M., ''Abstract algebra'' (Third edition), John Wiley & Sons, Inc., Hoboken, NJ (2004).</ref> but there are, up to group isomorphism, only four groups of order <math>8</math> containing a normal subgroup of order <math>2</math>  with quotient group isomorphic to the [[Klein four-group]].