Given a homomorphism $f$, one must always salivate, like Pavlov's dog, by asking for its kernel and image; once these are known, there is a normal subgroup and $f$ can be converted into an isomorphism.

This colorful remark can be found in J. J. Rotman's An introduction to the theory of groups (last paragraph on page 35 of the 4th ed. of the book)... I recalled it recently as I was reading of the 172nd anniversary of Ivan Pavlov's birth.