Steering wheel shake

I'm kinda stumped on this one. I have an 05 g6 3.5
At low speeds (around 40 kilometers per hour) there is a slight shake in the steering wheel.
It doesn't occur at very low speeds, and doesn't occur at speeds above 50kph.
The car was just inspected, and got a pass. This leads me to believe that no front end parts need replacing. With that said...I had the front tires balanced, which didn't help. My next thought was a possible bent rim. So...I rotated the tires. Still no luck.
Any help would be appreciated.

what type of inspection do they use ie hands on or a drive through??
when the tires were bal. did you let them no of your problem??

Not sure which is which. I guess it was a drive through inspection. They didn't take it on the road...If that's what you mean. Still.. very stringent. (I think)
I did not let them know of the problem. I probably should have, but opted for on-line advice.

i'm in delaware there is no put it on a lift pulling wh ck. fr end etc.if you have this kind of insection then have a tech check the front end

Does this happen when you're braking? if so, it's probalby that your brake rotors are warped. GM uses very cheap rotors on the G6.

a shake while driving could an alignment issue, an unbalanced wheel(s), loose lug nuts... then it could go more in depth such as a failing wheel hub bearing or other front end parts. Your best bet is to take it to the dealer or a shop that does wheel work on cars to find out what's going on.