The great division (v. 35) was just two groups: the Nephites, the true believers in Christ; and the Lamanites, those who rejected the gospel (v. 38). This is usually interpreted to be a philosophical difference, but the Lamanites made three additional divisions among the Nephites: Jacobites, Josephites, and Zoramites. The four divisions were the same as the original division after the death of father Lehi (see 2 Nephi 5:5–6). The Lamanites at this time had three divisions among themselves (4 Nephi 1:38): Lamanites, Lemuelites, and Ishmaelites. These divisions were the same as originally designated after the death of Nephi.
12 And it came to pass that Nephi died.
13 Now the people which were not Lamanites were Nephites; nevertheless, they were called Nephites, Jacobites, Josephites, Zoramites, Lamanites, Lemuelites, and Ishmaelites.
14 But I, Jacob, shall not hereafter distinguish them by these names, but I shall call them Lamanites that seek to destroy the people of Nephi, and those who are friendly to Nephi I shall call Nephites, or the people of Nephi, according to the reigns of the kings. [Jacob 1:12–14]
The seven designations at this time, along with the Lamanite teachings that they should not believe, even as their fathers, and that they taught their children to hate the children of God, even as their fathers (4 Nephi 1:38–39), implies a bloodline separation. While the philosophical difference was the significant one, there was still some recognition of the bloodlines, which would be expected. We know these bloodlines were still in existence even after the Lamanites had completely destroyed the Nephites as a nation. Those who were not destroyed were numbered among the Lamanites (see Alma 45:14; Moroni 9:24). Modern revelation also confirms that all seven of these original groups among the Nephites and Lamanites are still in existence today.
16 Nevertheless, my work shall go forth, for inasmuch as the knowledge of a Savior has come unto the world, through the testimony of the Jews, even so shall the knowledge of a Savior come unto my people—
17 And to the Nephites, and the Jacobites, and the Josephites, and the Zoramites, through the testimony of their fathers—
18 And this testimony shall come to the knowledge of the Lamanites, and the Lemuelites, and the Ishmaelites, who dwindled in unbelief because of the iniquity of their fathers, whom the Lord has suffered to destroy their brethren the Nephites, because of their iniquities and their abominations.
19 And for this very purpose are these plates preserved, which contain these records—that the promises of the Lord might be fulfilled, which he made to his people;
20 And that the Lamanites might come to the knowledge of their fathers, and that they might know the promises of the Lord, and that they may believe the gospel and rely upon the merits of Jesus Christ, and be glorified through faith in his name, and that through their repentance they might be saved. Amen. [D&C 3:16–20; see also 10:45–52]
The importance of verifying the bloodlines is to show that the final promises of the Lord to the various children through father Lehi, and others, of their never being destroyed are being fulfilled today (see 2 Nephi 4:6–11; 9:53).