Quotient group | 🗖 nosplit | ↑ parent "Subgroup" | 40, 10, 841

🗖 nosplit | ⇓ toc | ↑ parent "Subgroup" | Wikipedia | 40, 10, 841

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

Does not have to be isomorphic to a subgroup:

This is one of the reasons why the analogy between simple groups of finite groups and prime numbers is limited.

Table of contents | 40, 10, 841
- 1. Subquotient | 61 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 2. Relationship between the quotient group and direct products | 297 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
- 3. Normal subgroup | 135, 7, 443 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
  - 3.1. Simple group | 46 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
  - 3.2. Classification of finite groups | 64, 5, 262 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
    - 3.2.1. Classification of simple finite groups | 83, 3, 96 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"
    - 3.2.2. Group extension problem | 102 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"

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