The Four Transitive Subgroups of $A_7$. I know that $A_7$ contains 3 transitive subgroups: $A_7, PSL(2,7), F_{21}$ (Alternating group of 7 elements, $PSL(2,7)$, Frobenius group of order 21). 
In studying the Galois group structure of degree 7 polynomials, it seems that there is a 4th subgroup of $A_7$ that is transitive. I cannot seem to locate anything to indicate what this 4th group is. 
Is there indeed a 4th transitive subgroup of $A_7$ distinct from the 3 I have listed above?

To answer my own question:
The four transitive subgroups of $A_7$ are as follows:
$$C_7, F_{21}, PSL(2,7), A_7$$
