NFL Connections #55, Answers
The full solution: all four groups and the 16 names, sorted from the easiest group to the trickiest.
Coached under Andy Reid
Doug Pederson, Matt Nagy, John Harbaugh, Ron Rivera
Coached under Bill Belichick
Josh McDaniels, Brian Flores, Eric Mangini, Bill O'Brien
Coached under Bill Parcells
Bill Belichick, Tom Coughlin, Sean Payton, Romeo Crennel
McVay and Shanahan tree
Matt LaFleur, Zac Taylor, Kevin O'Connell, Mike McDaniel