The thrust of all this is simply that with priesthood comes order. That part of the Book of Mormon that has been granted to us makes no special effort to detail church organization among the Nephites. This, however, gives no justification for the idea that organization, discipline, and order were missing- where the priesthood is, they are also. (See Alma 13:1-16.)
“His Holy Order”
The phrase “his holy order” refers to the higher or Melchizedek Priesthood. Anciently this priesthood was called “the Holy Priesthood, after the Order of the Son of God. But out of respect or reverence to the name of the Supreme Being, to avoid the too frequent repetition of his name, they, the church, in ancient days, called that priesthood after Melchizedek, or the Melchizedek Priesthood.” (D&C 107:3-4.)
Where the priesthood of God is found, discipline and order will be found also. The government of heaven is a government of order. The scriptural account of Melchizedek’s ordination, for instance, states that he was
“ordained an high priest after the order of the covenant which God made with Enoch, it being after the order of the Son of God; which order came, not by man, nor the will of man; neither by father nor mother; neither by beginning of days nor end of years; but of God; and it was delivered unto men by the callings of his own voice, according to his own will, unto as many as believed on his name.”
(JST, Genesis 14:27-29)