The Firebeards were a tribe of Dwarves who came from the Blue Mountains. They were paired in habitat with the Broadbeams,  but each tribe had its own mansion. Tolkien, however never specified if the Firebeards lived in Nogrod or Belegost.
After the host of dwarves from Nogrod was defeated by the elves of Ossiriand and the Ents led by Beren there is no more mention of Nogrod and Belegost in the Silmarillion but in Appendix A of Return of the King it is stated their people fled with the dwarves of Belegost to Khazad-dum and swelled its ranks. At the start of the War of the Dwarves and Orcs, the houses of the other Fathers of the Dwarves were called upon by Durin's Folk. Since they had been joined with Durin's folk after the ruin of Beleriand and Thrain II Durin's Heir made his home in the remains of the ancient halls of the Firebeards in the Blue Mountains they were among the first to heed the summons. When Gandalf goes to the halls of Thorin Oakenshield they are in the ruins of Nogrod and Belegost.