In this case, your iPhone functions almost like an iPad—you should swipe down from the top right corner to access the Сontrol Сenter.
That's all there is to it :)
Important: You will need to swipe fairly close to the right corner to activate Control Center. Just swiping on the right half of the display won't do the trick.
This functionality might be really useful while surfing the web or just playing games on your iPhone :)