Lot of it is cache and search history. Go to Settings > Apps > Google > Storage > Clear cache. Then click on manage storage and clear search data ( note search history in Google Chrome will be eliminated).
Maybe this is the size of the Google app. You can clear the cache of the app to look at its original size.
@SAVVYSCLUTTER: It's quite typical for browser and media apps to be a few hundred MegaBytes (Samsung Internet is also around 400MB). I can't clarify exactly why the apps are that size specifically, however it shouldn't cause you too many issues with your storage if you have 64GB of internal memory.