Morogh was the first chief of the clan after their final expulsion from Uí Briúin Seóla.
King Áed in Gai Bernaig of Connacht had begun their subjugation in 1051, but it was only with the encastallation of Muintir Murchada under Richard Mor de Burgh that the family were finally driven to the west side of Lough Corrib.
The rest of their history as an independent people would be as rulers of Iar Connacht, or as it is now known, Connemara.
Moroghand and his brother, Ruaidhri, his brother may have accompanied Felim mac Cathal Crobderg Ua Conchobair (reigned 1233–1256), on an expedition to Wales in 1245 under Henry III.
This would have been on Henry III's campaign against Prince Dafydd ap Llywelyn of Gwynedd.