How to point subdomains?

I am running a minecraft server, a dynamic map add-on, and a website (using apache on computer to host website), all off of the same machine. I only have one public IP from my ISP and only one local IP assigned from router. All of these different things are using the one public IP but are on different ports. example, I have the Minecraft game using 12.34.56.78:1111, the map using 12.34.56.78:2222 and the website using 12.34.56.78:3333. I want to create a domain so I do not have to keep typing in the IP. And to complicate things further I want to add subdomains that redirect to the respective destination. What I would like to do is have game.mywebsite.com go to 12.34.56.78:1111 (Minecraft server), map.mywebsite.com go to 12.34.56.78:2222 (dynamp map) and www.mywebsite.com (or wiki.mywebsite.com if it makes things easier) to go to 12.34.56.78:3333 (website). I have talked with my local telephone company who offers domain registration and unlimited subdomains and they said they can register the subdomains but they are unable to point them to specific ports. They said this is something done host side. How would I go about configuring my equipment to do what I am trying to do, and what would I configure? Is this something that is done by the router, my computer, Apache, or a combination of them. Can someone help me out? I am new to all of this, so while I understand basic port forwarding and basic router config, please try to explain it as detailed as you can.

I appreciate any information you can give me.

Please and Thanks,

goosar19