And what "grouping" would that be? Does "it" have a name?
Sure. One form would be "baptsts" who were the form of gathering even during Jesus' earthly ministry of preaching first John Baptist's kingdom of heaven, then after John's death only the Kingdom of God.
Another would be those following the New Covenant doctrines cited by Donatus, a pastor at Carthage, that forced the Catholic infant-baptizing heretics out into the open.
Another would be the reconstruction of genuine local New Testament assemblies adopting the general form suggested by John Nelson Darby and his friends. John was trained as an Anglican, but rejecting episcopacy as a form of church government. Such assemblies are commonly referred to as "Plymouth" brethren, after the locality in England where such assemblies first emerged in the mid-1800s.
But if you had studied the history of Christianity, you would have known about these groups.