Symmetric Group on 4 Letters/Subgroups/Examples/Even Permutations

Example of Subgroup of Symmetric Group on 4 Letters
The subset of the Symmetric Group on $4$ Letters $S_4$ which consists of all the even permutations of $S_4$ forms a subgroup of $S_4$.

From Alternating Group is Set of Even Permutations, this is by definition the alternating group on $4$ letters $A_4$

Its Cayley table can be presented as follows:

As $A_4$ has index $2$, it is normal in $S_4$ from Subgroup of Index 2 is Normal.

Hence the quotient group $S_4 / A_4$ is cyclic of order $2$.