The published Silmarillion tells us almost nothing of Ingwë's family, except that he was closely related to Indis. Various sources within The History of Middle-earth tell us more: in The Later Quenta Silmarillion (in volume 10) we're told that he had many children, and in The Shibboleth of Fëanor (in volume 12) Indis is stated to be the daughter of his sister. Tolkien's ideas on this topic changed over time (at one point Indis was Ingwë's sister) but the genealogy shown here follows the latest formulation.
One important member of Ingwë's family was his son Ingwiel, who is prominent in early stories of the War of Wrath. According to those tales, it was Ingwiel who led the Vanyar to Middle-earth, sailing across the Great Sea and landing at Eglarest, where he defeated the Orcs who held the Haven. In the published Silmarillion, Ingwiel has disappeared, and only Finarfin is named as a leader of the armies of the Elves. In volume 4 of The History of Middle-earth, Christopher Tolkien suggests that this omission may have been an error, and Ingwiel should have remained in the text as joint commander of the Elves of Valinor.