 Fundamental theorem on homomorphisms

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

Links group homomorphism and the quotient group via normal subgroups.

The Fundamental Theorem on Homomorphisms, often referred to in the context of group theory or algebra in general, states that there is a specific relationship between a group, a normal subgroup, and the quotient group formed by the subgroup. In summary, it describes how to relate the structure of a group to its quotient by a normal subgroup.