As Commander in Chief of the US military (as determined by the Constitution), it makes sense for him to have that power. However, shutting down parts of the Int

As Commander in Chief of the US military (as determined by the Constitution), it makes sense for him to have that power. However, shutting down parts of the Internet is unconstitutional because as far as I'm aware, it doesn't grant that power to the President (and by "that power", I don't mean specifically shutting down the Internet. I mean the idea behind it).