Iorwerth gives a good summary in his [i:185y7cpa]Beer and Cider in Ireland[/i:185y7cpa].
Heineken became the sole owner in 1983. Before that it was mostly owned by the State via Taiscí Stáit Teo. (the State Rescue Company). A publicans' collective called the Licensed Vintners Cooperative Society owned just under half of the company from 1974.
The State had bought the company from Watney Mann in the early 1970s (thank you Taoiseach Lynch), and Watney's had taken the controlling interest from the Murphy family in 1967, having bought 30% of it a few years earlier.