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  "body": "\n## Summary\n\nA subnormal subgroup is joined to the whole group by a finite chain of subgroups, each normal in the next.\nEvery normal subgroup is subnormal, but not conversely, because normality is not transitive.\nSubnormal subgroups are exactly the subgroups that occur as terms of subnormal series, and they are central in the structure theory of finite groups.\n\n## Explanations\n\n### L1 human\n\nBeing normal is a relation between a subgroup and a bigger group.\nIf $H$ is normal in $K$ and $K$ is normal in $G$, then $H$ need not be normal in $G$.\nA subnormal subgroup is one that reaches the whole group in finitely many such normal steps.\nFor example, in the alternating group $A_4$ the subgroup $\\{e, (1\\,2)(3\\,4)\\}$ is normal in the Klein four-group, which is normal in $A_4$.\nSo it is subnormal in $A_4$, even though it is not normal in $A_4$.\n",
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