Hawaiian geese are surprisingly closely related to Canada geese.
In fact some subspecies of Canada geese are genetically closer to the nene than they are to other subspecies of Canada geese.
The split between Canada geese and Hawaiian geese has most likely taken place as recently as only half a million years ago, after which the nene has evolved into a herbivorous bird with a distinct coloration. The nene still can fly, just not as well as the Canada goose, but some of its now extinct relatives were completely flightless.
The rapid evolution of Canada goose into the nene is an example of how quickly a species can change under the right circumstances.
The Hawaiian goose or nene is the official state bird of Hawaii.
State Bird of Hawaii Unmasked as Canadian.
Hawaiian Goose (Branta sandvicensis) on birdlife.org.