I’m guessing you’re not actually trying to logon to your router, but
rather configuring your router so that you can use the connection to
the internet provided by your ISP.
Exactly how we do what we do next depends on the specific router, so
I’ll use mine as an example.
But here’s a hint: none of it depends on knowing a subnet.
As you point out, there are several pieces of information your router needs in order to provide your internet connection:
Your IP address – this uniquely identifies your internet connection, and is actually the IP address of the router on the internet.
The subnet mask – a somewhat mysterious number that actually lets your router know what other IP addresses are “nearby”
The gateway address – the IP address of the upstream device – the “gateway” to the rest of the network – to which your router should send packets for devices that aren’t “nearby”
Here’s the trick: in the vast majority of consumer, home and even small business connections you never have to know any of this. It’s all provided automatically.
Routers can be configured to use several different approaches to connecting to your ISP. The most common is called “DHCP”, or what’s referred to by my LinkSys above as “Obtain an IP automatically”. That’s actually a tad misleading, since the router then gets not only the IP address, but all the other information I listed above, automatically, from your ISP.
You don’t have to enter a thing.
Which, of course, is why it’s the most common approach.
The opposite end of the spectrum is the “static” IP. When using a static IP, the IP address you should use, as well as all of the other information, is provided by your ISP. Be it in an email, some web instructions, or over the phone – this information is provided by the ISP so that you can then manually configure your router.
You don’t have to “find it”, you don’t have to “figure it out”, you just enter the information that’s been provided by your ISP, or contact them if you’ve not received it.
The real problem, of course, is that when configuring a static IP to connect to the internet you can’t figure it out on your own. All of these values are assigned and defined by your ISP.
If you find yourself in a position where you think you need to configure a static IP address, check with your ISP for what they expect you to do.