Your Factorio server might not be showing up in the server list for a variety of reasons. Here we are going to go through the common reasons why your server might not be in the list.
Server is not listed to public.
Your server has a setting "Publicly Visible". For your server to appear in the server list you must set this to "Yes" in your server settings.
Authentication details are missing.
Servers must be authenticated in order to show up in the public servers list. Make sure you have entered your Username and Password/Token, and validate the login worked by checking your server logs.
Your server is having an issue connecting to the Internet.
Your server must register itself with the Factorio auth servers in order to appear in the list, Check your server's console output and ensure there are no errors in regards to connecting to the internet.