Rabbi Chaim Schneur Zalman was the son of Rabbi Menachem Mendel Schneersohn (the third rebbe of Chabad-Lubavitch), and became a rebbe in his own right for a number of Chabad Chasidim following his father's passing.
After the passing of Rabbi Menachem Mendel Schneersohn (the third rebbe of Chabad-Lubavitch), several of his sons independently assumed the role of rebbe.
Rabbi chaim Schneur Zalman assumed the role of rebbe in the Liadi, the same town his great-grandfather, Rabbi Shneur Zalman of Liadi (the first rebbe of Chabad-Lubavitch), was rebbe.
Rabbi Chaim Schneur Zalman was succeeded by his son, Rabbi Yitzchak Dovber of Liadi.
Additional members of Schneersohn family are not listed here