One of the teleport devices on floor 3 will transport you to floor 7, in a room where you will battle your rival. From there, go around the table to the next teleport dvice. It will transport you to floor 11, and you will have to fight 1 rocket grunt before facing Giovanni. Then, use the card key to open the door, and Giovanni will be there. Beat him, and the Rockets will evacuate Silph Co.