What three groupings did the Jews put the Old Testament into?

The Jewish Bible is not the Old Testament, it is the Tanach. Within the Tanach, there are three sections which are: Torah (Teachings), Nevi'im (Prophets), and K'tuvim (Writings).

The Christian Old Testament was based on the Tanach, however, it was altered throughout to support the teachings of Christianity. One of the alterations was the order of the books which render the Jewish categorization inapplicable.