Cosets | Normal subgroups | Quotient Groups/Factor Groups

This video tries to simplify the idea of cosets and factor groups.
At @26:15 , I got confused between K4 and Z4 as the 4th element in both the groups is a combination of 2nd and 3rd element, but the difference is that the order of all elements is 2 in K4 while in Z4, that order is different i.e. |a| = 4 while |a^2| = 2. Also, a^3 is not self invertible.