Hummm, If I understand correctly, the 192.168.1.XXX is your private IP address in LAN, and you probably have a public IP address, which your ISP gives you. So just to be clear in your DNS record you should have your public IP address set to point to your subdomain, not your private ip address (in LAN), and secondaly your router might need to be configured to allow incoming traffic route it, to your private IP 192.168.1.XXX. And your ISP should allow incoming traffic
Alternative you can just tunnel your local traffic to a remote server so that you don’t need to mess with your router setting or think if your ISP allows incoming traffic.
So what is your case, tunnel traffic, or allowing incoming traffic via NAT or DMZ?