Source: /cirosantilli/quotient-group

= Quotient group
{wiki}

Ultimate explanation: https://math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426\#3732426

Does not have to be isomorphic to a subgroup:
* https://www.mathcounterexamples.net/a-semi-continuous-function-with-a-dense-set-of-points-of-discontinuity/
* https://math.stackexchange.com/questions/2498922/is-a-quotient-group-a-subgroup
This is one of the reasons why the analogy between <simple groups> of finite groups and <prime numbers> is limited.