Assalaamu alaykum. I was wondering, why does the Quran not mention ‘Aad, Thamud, and Shu‘aib among the decentants of Noah?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Perhaps by mentioning ‘Aad, you mean the Prophet who was sent to them, which is Hood (Hud),  and by Thamood, perhaps you mean the Prophet who was sent to them, which is Saalih . In fact, we did not find statements from the scholars regarding the wisdom behind not listing them among the descendants of Nooh (Noah) like the verses in Soorah Al-An‘aam (Chapter 6), assuming that the pronoun in the verse {his descendants} refers to Nooh and not to Ibraaheem (Abraham) as some scholars said. What is common between these three Prophets is that they were all Arabs, and the only Arab Prophet mentioned in these verses is Ismaa‘eel (Ishmael) . However, the verses do not mention all the descendants inclusively, as is clear from the use of the preposition 'of' in {and of his descendants...} [Quran 6:84] So the verses do not intend to list all the descendants of Nooh, as, in fact, his descendants, and especially the Prophets thereof, are more than those mentioned in the verses. Where then is our Prophet Muhammad, sallallaahu ‘alayhi wa sallam, and where are Idrees (Enoch), Is-haaq (Isaac), Ya‘qoob (Jacob) and Thul-Kifl, may Allaah exalt his mention?

We would like to emphasize that the Muslim should concern himself with asking about matters that lead him to do good deeds, what is needed for adhering to the sound Islamic creed, the validity of the acts of worship or transactions and interactions with people, or what is related to ethics and good manners.

Allah knows best.