We had this discussion acouple of days ago. The "correct" spelling is AUBRIETIA, but Google also recognises AUBRIETA. AUBRETIA is wrong, because the genus is named after a botanist called Aubriet.
Two more plants genera that are almost invariably spelled incorrectly are FUCHSIA (named after Fuchs, so not FUSCHSIA) and WISTARIA (named after Wistar, so not WISTERIA)!