Conrad I is one of four siblings
Judith, Udo, Konrad and Heribert. There parents are unknown but but theories connecting them to two brothers, Konrad and Udo, sons of Gebhard. Both theories have problems and lack evidence and a third unknown man may actually be father.
Conrad I married once (refer to Justin's Discussion connected to this profile regarding her identity) to a woman commonly identified as Richlint.
Conrad I was succeeded by his son Hermann II.
Sources suggest Conrad I had 8 other children: Ekbert, Luitpold, Liutold, Konrad, Ita, Adelia, Judith, Kunniza.
The profile that this Discussion is started from appears to be a mixture of Conrad I and his possible father (Konrad son of Gebhard), so this children are a mixture of Conrad I's children, Conrad I's siblings and someone named Arnold(?).
Looking at Arnold's revision history suggests that he is the son of a Judith, Conrad, Konrad and Udo are all linked to wives potentially named Judith and Arnold's mother could be any of these women or just another Judith randomly confused during merging. If you follow the same Revision history on Arnolds profile you find his fathers name was originally Rhinegau but that profile has been merged into Conrad I... remember Conrad I married Richlint NOT Judith (maybe:)
Following Arnold's revisions also reveals a daughter, Auxilia, and her profile sheds some light. But don't expect me to type it all here!