Here is the problem in the text, I have a specific quetsion about it:

WOrk out the left and right cosets of H in G when G=A4 (alternating group that permutates 4 numbers)

H={e,(12)(34),(13)(24),(14)(23)}

and

G=A4 H={e, (123), (132)}

Okay, I know how to find cosets, my question here is whether I need to go through all the work of finding the cosets of each element in G. My idea is that LaGranges theorem tells us that |G|/|H| gives us the number of unique cosets, so I only need to work out the 4 unique cases. Am I correct here?