He married Maud, an illegitimate daughter of King Henry I of England before 1113. Conan and Maud had three children that are known:
Hoel (1116–1156) – disinherited from the ducal crown; Count of Nantes;
Bertha (1114 – after 1155) – married Alan of Penthièvre; upon Alan's death in 1146, she returned to Brittany;
Constance (1120–1148) – married Sir Geoffroy II, Sire de Mayenne, son of Juhel II, Seigneur de Mayenne.
Succession
On his death-bed in 1148, Conan III disinherited Hoël III from succession to the duchy, stating that he was illegitimate and no son of his. By this surprise move Bertha became his heiress and successor. However, Hoël III was to retain the County of Nantes.
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Everard, J. A. (2004). Brittany and the Angevins: Province and Empire 1158–1203. Cambridge University Press.
Warren, Wilfred Lewis (1977). Henry II. Yale University Press.