The 192.168.1.1 IP address used by many home routers is an IANA-reserved private network address or subnet.
What's a subnet? An entire range of IP addresses that you can split up into a smaller ranger (the act of splitting it up is called subnetting) if you want.
So the above range is 192.168.0.0/16. Keeping it simple without getting too much into the individual bits, each "octet" or individual number in the address is 8 bits, and the ones that are "yours" start from the right. So that means the last two octets (16 bits) are yours to do whatever you want. So you can use all the IP addresses from 192.168.0.1 to 192.168.255.254 (the first one is reserved and the last one is a broadcast address) really in any way you want and your router allows.
The simplest route usually taken in this situation is to use the "sub-subnet" 192.168.0.0/24 or 192.168.1.0/24. Using 192.168.0.0/24 as an example, this means your home network can use any IP address from 192.168.0.1 through 192.168.0.254, with 192.168.0.255 being the broadcast address.
But you are free to change the subnet, since you have two numbers that are really "yours", so you can use 192.168.44.0/24 or any other number for the second octet. Just keep in mind that everything that needs to see each other on the network needs to be on the same subnet (i.e. within that subnet's range of IP addresses). So your router's IP address needs to appear in that subnet (good choice is 192.168.44.1), and your router needs to give out DHCP addresses from a range in that subnet (say something like 192.168.44.10 through 192.168.44.50).
Nothing is really stopping you from using 192.168.0.0/16 for your home router either, but it's good practice to leave some room for additional networks or changing things in the future.
1I generally recommend that folks with home networks just use 192.168.XX.0/24 where XX is between 10 and 245. perhaps the last two digits of the year of your birth? Any number in that range works.
"69 dudes!" -- Bill S Preston Esqr and "Ted" Theodore Logan – Frank Thomas – 2015-04-24T12:50:32.730
17@DavidGrinberg Hopefully, you'll never need to visit that range then. That range is assigned to a company called Xerox. – phyrfox – 2015-04-24T14:25:09.703
11If 10.0.0/24 traffic is going to Brazil, your ISP is doing something very weird, and you should call them out on it. Except with special arrangements between the parties involved, 10/8 (like the other RFC 1918 ranges) is supposed to never make it past the egress router of a network. – a CVn – 2015-04-24T17:17:51.543
@MichaelKjörling, the exception is that as an ISP client, you are considered to be part of their private network. So, if the ISP's network spans internationally (such as Brazil) you can potentially reach a 10.0.0.0/8 address in another country. While it is generally good design to minimize this exposure to clients, this is an increasing trend as ISPs run out of PI IP space to use on their internal networks. – YLearn – 2015-04-24T18:14:19.723
Very weird IMO for your company to be using 192. 172 or 10 are typical in companies with any kind of knowledgeable IT department. – paqogomez – 2015-04-24T22:22:39.347
@paqogomez: Using 192 would make sense for a small company. Being well-informed has little to do with it. – martineau – 2016-09-19T23:56:42.920
That is weird that they would conflict that way. The VPN should have NAT'ed you or otherwise allowed 2 private networks be used on either side of the pipe. It had to be a COMMON conflict considering that 192.168.0 is the most used default network for cheap residential routers... – GB - AE7OO – 2020-01-10T14:32:05.447