Alternating group A_4

The alternating group $A_4$ consists of the even permutations of $\{1,\ldots,4\}$ , with composition as multiplication.

Order and simplicity

Its order is $12$ . The subgroup $\{1,(12)(34),(13)(24),(14)(23)\}$ is a normal Klein four-group, so $A_4$ is not simple.

References

J. S. Milne, Group Theory, v4.01, §4, symmetric and alternating groups; Theorem 4.33 and Remark 4.34, p. 69.