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  "body": "\n## Example\n\nIn the [[symmetric group|0515A6D2Y1]] $S_3$, let $H = \\{e, (1\\,2)\\}$. Compose permutations from right to left.\nThe [[left cosets|05FD317V2W]] of $H$ are $eH = \\{e, (1\\,2)\\}$, $(1\\,3)H = \\{(1\\,3), (1\\,2\\,3)\\}$ and $(2\\,3)H = \\{(2\\,3), (1\\,3\\,2)\\}$.\nEach of the $6$ elements of $S_3$ is in exactly one of these cosets.\nEach coset has $2$ elements. Thus $6 = 3 \\cdot 2$, as [[Lagrange's theorem|3C53TD]] states.\n\n## Remarks\n\nThe right cosets of $H$ are different sets, because $H$ is not normal in $S_3$.\n",
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