If it only happens at highway speeds (around 50-65 mph or so) it is usually a wheel balance issue. If it is happening at most speeds, it could be the wheel hub bearing or something related to the suspension. If it were mine, I would jack the front wheel up try to wiggle it top to bottom and side to side to see if there is any movement or play in the wheel. I would also remove the wheel and check to see if anything looked obviously broken on the suspension or wheel hub. This would also have the side effect of checking more mundane things like the wheel being put back on right and the lug nuts being tight.
Does you G6 have hydraulic or electric power steering?
Does you G6 have hydraulic or electric power steering?