Hungerford -Algebra p.271
Let $E/F$ be a Galois extension where $E$ is a splitting field for a separable irreducuble polynomial $f$ over $F$ whose roots are $a_1,a_2,a_3$.
Let $\Phi:Gal(E/F)\rightarrow S_n$ be the natural group monomorphism permuting roots of $f$.
Then the order of '$Gal(E/F)$ is divisible by $3$, henve it is a normal subgroup of $S_3$.
These are all I know. How do I prove that the Galois group is eithet S3 or A3?