Jesus entered the human family through the Promised Son of Abraham, Isaac. The Scriptures are painfully clear about this, showing how Abraham, Sarah, and Hagar tried to manipulate the plan of God, and help God keep His promise by creating an alternate plan.

By Abraham's relationship to the servant of his wife, Ishmael came into the world. Ishmael was first indeed, but not the promised son. Not the one who would bring Messiah and bless all nations. All of those blessings would devolve upon Isaac.

But in Koranic teaching, it was Ishmael who was offered on the Mt. Moriah altar, and in reward for this heroic act, God gave Isaac to Abraham. Christians recall that the Scriptures indicate that the offered son was Isaac.

Muhammad claims, perhaps rightly so, a family connection to Ishmael. Genealogies offered by a number of Muslim scholars have differed from one another. Numbers and names don't match up. It is impossible to tell at this point which one is correct. Here is my series of lists to add, hopefully, to the resolution of some of the chaos. First I offer the list given by Lings and continued by Wikipedia.

A. From Muhammad to the early tribal leader of his people, Quraish, is as follows: (Per Lings)

Muhammad ,Abd Allah, Abdul Mutallib (who was called Shaiba), Hashim (named ‘Amr, after whom the Banu Hashim clan was named), Abd-e-Manaf (called Al-Mugheera), Qusai (Qusayy) (also called Zaid), Kilab, Murra, Ka'b, Luwai (Lo’i), Ghalib, Fihr (known as Quraish and whose tribe was called after him).

B. Thus far does Lings dare to go in his work. From Wikipedia I glean the continuation of the line between Fihr (Quraish) and Ishmael. No one swears by this line, but there is possibly some validity to it:

Malik, an-Nadr (also called Qais), Kinana (founder of the largest Adnanite tribe of western Saudi Arabia in Hijjaz), Khuzaima (Khuzaiman), Mudrika (who was called ‘Amir), Ilyas (Elias), Mudhar (Muzar) (patriarch of one of the two main branches of the "North Arabian" Adnanite tribes), Nazar (Nizar), Ma'ad, Adnan (ancestor of the Adnani Arabs of northern, central and western Arabia), Udad (Awwad), Al-Muqawwim, Al-Yas'a, Al-Hamis (Al-Humaisa), Nibt (Nobet), Salaman (Sulayman), Hamal (Haml), Qidar (Qaidar) (father of the North Arabian Qedarite tribe that controlled the region between the Persian Gulf and the Sinai Peninsula), Isma'il (Ishmael).

C. Both of these last names, Quidar (Kedar in NKJV) and Ishmael, are quite Biblical, as is the rest of the line, from Abraham to Adam, which matches clearly the genealogies in Chronicles 1:1-27 and Luke 3:34-38, though spelling variants do not make this obviously clear at first.

Ibrahim Khalil-Ullah (Abraham), Ta'rikh (Azar), Tahur, Shahru, Abraghu (Ra‘u), Taligh (Falikh), Abir, Shale' (Shalikh), Arfakhad , Arfakhshad), Sam - the Semitic family/race, which encompass a large group of families, Nuh (Noah), Lumuk (Lamik), Mutu Shalkh (Mutwashlack), Akhnukh (who is said to be Prophet Idris), Yarad (Yarid), Mahla'il, Qinan (Qainan), Anush (Anusha), Sheeth, Adam Abu'l-Bashar (Adam).

D. Here is a line-up of this part of the genealogy, from the three faiths, also borrowed from Wikipedia but also from the Scriptures.

Jewish(Chronicles)

1. Adam

2. Shet

3. Enosh

4. Kenan

5. Mahalalel

6. Yered

7. Chanokh

8. Metushelach

9. Lamekh

10. Noach

11. Shem

12. Arpakhshad

13. Shelach

14. Ever

15. Peleg

16. Re'u

17. Serug

18. Nachor

19. Terach

20. Avraham

Christian (Luke)

1. Adam

2. Seth

3. Enos

4. Cainan

5. Mahalalel

6. Jared

7. Enoch

8. Methuselah

9. Lamech

10. Noah

11. Shem

12. Arphaxad

13. Cainan

14. Shelah

15. Eber

16. Peleg

17. Reu

18. Serug

19. Nahor

20. Terah

21. Abraham

Islamic (Ibn Ishaaq)

1. Adam

2. Sheeth

3. Yaanish

4. Qaynan

5. Mahlil

6. Yard

7. Akhnookh

8. Mattooshalakh

9. Lamk

10. Nooh

11. Saam

12. Arfakhshadh

13. Shaalikh

14. Aybar

15. Faalikh

16. Raa'oo

17. Saaroogh

18. Naahoor

19. Tarih

20. Ibraheem

The line of Jesus is simpler, although many have struggled with these genealogies in the Bible. You will see above the direction Muhammad takes from Abraham, namely through Ishmael.