This chapter covers the descendants of David through the time of the end of the captivity. In the family tree outline I have placed the name of David in red since he is an ancestor of Jesus Christ but I put the names of the kings that followed him, beginning with Solomon, in purple. This is necessary to show that Jesus does not claim the throne of David through the kingly line, through whom His guardian, Joseph, was of direct male lineal descent. Jesus has a blood tie to David through His mother, Mary, who descended from David's and Bathsheba's son, Nathan.
There are a few names that I could not place within the genealogy because there is not enough information given. However, it is clear from the context that these are descended from David and perhaps the author of the chronicles and his contemporary readers knew the connection.
34. Amnon (mother: Ahinoam the Jezreelitess; born in Hebron)
34. Daniel/Chileab (mother: Abigail the Carmelitess; born in Hebron)
34. Absalom (mother: Maachah the daughter of King Talmai of Geshur; born in Hebron)
34. Adonijah (mother: Haggith; born in Hebron)
34. Shephatiah (mother: Abital; born in Hebron)
34. Ithream (mother: Eglah; born in Hebron)
34. Shimea (mother: Bathsheba, the daughter of Ammiel/Eliam; born in Jerusalem)
34. Shobab (mother: Bathsheba the daughter of Ammiel/Eliam; born in Jerusalem)
34. Nathan (mother: Bathsheba the daughter of Ammiel/Eliam; born in Jerusalem)
34. Solomon (mother: Bathsheba the daughter of Ammiel/Eliam; born in Jerusalem)
52. Salathiel*cf Matt. 1:12
54. Shelomith (f.)
34. Tamar (female; mother: most likely Maachah)
The following are descended from David but I have no idea where they fit into the genealogy (verses 21-24). They could possibly be 4 sons of concubines such as are mentioned in verse 9 with the notation "besides the sons of the concubines, and Tamar their sister."
Rephaiah and his sons
Arnan and his sons
Obadiah and his sons
1. Shechaniah and his sons