The integers modulo the even integers

Example

Let $G = (\mathbb{Z}, +)$ be the integers with addition, and let $N = 2\mathbb{Z}$ be the even integers. $N$ is normal, because $G$ is abelian. $N$ has two cosets: $N$, the even integers, and $1 + N$, the odd integers. The sum of two odd integers is even, so $(1 + N) + (1 + N) = N$. Thus the quotient group $\mathbb{Z}/2\mathbb{Z}$ has two elements, with identity $N$. It is the integers modulo $2$.