Sarah, just a bit more work to see every stop on the run on the Trenitalia site. First, as Steve says above, these are the stops just in Genoa. Second, there are other runs farther down that have fewer stops. However, if the 7:11am run is one you wish, it still gets you there in good time.
Third, click on the SELECT button on the right and then click on DETAILS BY SELECTION as Steve mentions above.
At this point, you still do not see all of the stops. In fact, you may not even see what happened when you clicked on DETAILS BY SELECTION. Unfortunately, Trenitalia will display the run but you often won't see it unless you scroll down. It's there. Next. click on the INFO button on the right and scroll down again. All of the stops will appear. Guaranteed. I do it all the time. Scrolling is the secret here.