*Conrad of Hesse Duke of the "Old" Franks
born 0845
died 27 February 0906 Fritzglas

father:
*Eudes II of Franconia
died about 0879

mother:
unknown

siblings:
*Gerhard II Duke of Lorraine died 29 June 0910
Eberhard Count of Nieder Lahngau

spouse:
*Glismut of Saxony
(end of information)

children:
*Conrad I Duke of Franconia King of Germany
born about 0890 Babenberg
died 23 December 0918 Germany
*Mathilda von Hesse born about 0899 Hesse, Germany
Eberhard of Franconia died after 0936 Babenberg

biographical and/or anecdotal:

notes or source:
ancestry.com
Eberhard of Franconia was definitely *Conrad of Franconia's brother (Encyclopedia Britannica).
However they are listed under different sources as having two different fathers.
Hence the confusion.