Turning off my alarm

So...noob question... how do I turn off my alarm when my phone is unlocked?

I've been using an old iPhone with an old iOS for the longest of times until it finally broke and I got a new one with iOS 10. Before, when my alarm sounded when my phone was unlocked, a small window will pop up with the options "snooze" and "stop." While this option still exists when the phone is locked (though I much prefer the swipe to the right to turn off the alarm as opposed to press that tiny text on the bottom of the screen...), now, when my phone is unlocked and my alarm goes off, it only shows up as a notification on my screen like someone texted me. When I tap on the notification, it automatically goes on snooze. Furthermore, the clock app is not in the notification center in the settings page...

So, how do I go about turning off my alarm if my screen is unlocked?