1. Determine the quotient...

I have a normal subgroup $K = \{id, (12)(34), (13)(24),(14)(23)\}$ and $G=S_4$.

How do I find the quotient $K / G$ ?

2. Originally Posted by MichaelMath
I have a normal subgroup $K = \{id, (12)(34), (13)(24),(14)(23)\}$ and $G=S_4$.

How do I find the quotient $K / G$ ?
You surely meant $G/K=$ the quotient group of G by K. Begin by calculating the quotient's order using Lagrange's Theorem, and then since there're only two groups up to isomorphism of that order, it'll be easier to check which one this quotient fits in.

Tonio