Who were the priests of the 2nd order?

2 Kings 23:

4 And the king commanded Hilkiah the high priest, and the priests of the second order, and the keepers of the door, to bring forth out of the temple of the LORD all the vessels that were made for Baal, and for the grove, and for all the host of heaven: and he burned them without Jerusalem in the fields of Kidron, and carried the ashes of them unto Bethel.

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What were these priests of the second order?

New International Version:

4a The king ordered Hilkiah the high priest, the priests next in rank and the doorkeepers to remove from the temple of the LORD all the articles made for Baal and Asherah and all the starry hosts.

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second in rank,
Strong's 4932: A repetition, a duplicate, a double, a second

Pulpit:

and the priests of the second order. Not the "deputy-high priests," of whom there seems to have been only one at this period of the history (2 Kings 25:18); nor the "heads of the courses," who were not recognized as a distinct class of priests till much later; but merely the common priests, as distinguished from the high priest. (So Keil, Bahr, and others.)

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According to Pulpit, there were only high priests and common priests:
priests of the second order = common priests

Barnes' opinion was similar:

The priests of the second order - This is a new expression; and probably refers to the ordinary priests, called here "priests of the second order," in contrast with the high priest

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The same Hebrew word is used to describe musicians in 1 Chronicles 15:

16 David told the leaders of the Levites to appoint their fellow Levites as musicians to make a joyful sound with musical instruments: lyres, harps and cymbals.
17 So the Levites appointed Heman son of Joel; from his relatives, Asaph son of Berekiah; and from their relatives the Merarites, Ethan son of Kushaiah; 18 and with them their relatives next in rank: Zechariah, Jaaziel, Shemiramoth, Jehiel, Unni, Eliab, Benaiah, Maaseiah, Mattithiah, Eliphelehu, Mikneiah, Obed-Edom and Jeiel, the gatekeepers.

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Here too, there seemed to be just two classes.

Who were the priests of the second order?

The Bible never mentions priests of the 3rd order. They were just the common priests.