If you signed up for Showtime in the Apple TV app for the Showtime channel,
or if you signed up for Showtime in the Showtime app on an Apple device,
then those would be listed in your subscription overview.
Subscriptions are listed there from the start of the trial period.
If you subscribed with Showtime directly or through a third party, then it would not be listed with Apple.
You can manage that on iPhone, iPad, iPod Touch, Mac, or Apple TV box.
You can manage that in the iTunes application on Macs with older OS and on current PCs.
You can manage Apple TV app channel subscriptions in the Apple TV app on third party devices.
You will need to sign in with the matching Apple ID account.
Many subscriptions require 24 hours notice for cancelation, else they will charge another billing period.
How to cancel:
- On any of your Apple devices: How to cancel a subscription from Apple - Apple Support
- On Apple TV (4th generation or later): Settings﹥Users and Accounts﹥[username]﹥Subscriptions﹥…
- On third party devices with the Apple TV app: Manage subscriptions in the Apple TV app - Apple Support
- On a PC with iTunes: Use a Windows PC to cancel subscriptions from Apple - Apple Support