Regarding Congruence Subgroups and Normal Subgroups of Finite Index of the Modular Group $PSL(2,\mathbb{Z})$ ($SL(2,\mathbb{Z})$)

Question

Let $PSL(2,\mathbb{Z})$ ($SL(2,\mathbb{Z})$) be the modular group.

It is too easy to see that every congruence subgroup of the modular group $PSL(2,\mathbb{Z})$ ($SL(2,\mathbb{Z})$) is a normal subgroup of finite index.

The question is whether the converse is also ture, i.e., is every normal subgroup of finite index of the modular group $PSL(2,\mathbb{Z})$ ($SL(2,\mathbb{Z})$) congruence subgroup of the modular group $PSL(2,\mathbb{Z})$ ($SL(2,\mathbb{Z})$)?