The largest family in my [direct] tree is: MINE!
My parents had 15 children, of which I am the 12th. I have 9 children of my own, the most of my siblings, all of whom survive except one.
But just yesterday I met a man who was one of the second largest family from the same parents of any living person I have ever met: he was the 7th of 17; his twin was the 8th
The winner, though, is that a few years ago I met a woman who told me she was 24th of 25, with no twins. She had only one daughter, but the average size of her siblings's families was 14, so her daughter had 252 going on 255 first cousins. Not even in genealogical sources have I seen a family as large as that, certainly not from one mother and father, and that was true for her.