The Laigin had suffered a crushing defeat at the Battle of Áth Senaig (Ballyshannon, County Kildare) in 738 at the hands of the High King Áed Allán mac Fergaile (died 743) of the Cenél nEógain.
Muiredach maintained good relations the High King of Ireland, Domnall Midi (died 763) of the Clann Cholmáin.
Muiredach's son Bran Ardchenn mac Muiredaig (died 795) married Domnall Midi's daughter Eithne.
[3][4] The Uí Máil branch of the Laigin had at times held the kingship of Leinster; the last being Cellach Cualann mac Gerthidi (died 715).
In 744 the final attempt by the Uí Máil was defeated at the Battle of Ailén dá Berrach in Cualu,[5] a district in County Wicklow.