At it's heyday the Irish mob was never that big

The infamous Westies were just 10-20 guys.

There were a few more sophisticated and large Irish mobs but none were even on par with a small LCN family. There was usually no structure in place thus when a bust or two happened the entire organization usually fell apart.

A lot of the Irish gangs, were very similar to Philidelphia in the 90s. Small groups of gangsters that grew up together with simple rackets and were ready to use violence whenever.