In Internet networking, a private network is a computer network that uses a private address space of IP addresses. These addresses are commonly used for local area networks (LANs) in residential, office, and enterprise environments. - Wikipedia

The Internet Assigned Numbers Authority (IANA) has reserved the following three blocks of the IP address space for private internets:

10.0.0.0    - 10.255.255.255  (10/8 prefix)
172.16.0.0  - 172.31.255.255  (172.16/12 prefix)
192.168.0.0 - 192.168.255.255 (192.168/16 prefix)

Internet Service Provider

My consulting business utilises a small business NBN plan (100/40 Mbps) and the provider supplied a Gateway (a modem-router combination) with support for FTTN.

The Gateway address is 192.168.20.1

Subnets

I want to divide my network into two or more subnets.

For example, devices connected to my ISP's Gateway will be allocated addresses in the range 192.168.20.2 - 192.168.20.254. Devices connected to my Synology NAS's eth1 port will be allocated addresses in the range 192.168.21.2 - 192.168.21.254.

ISP Gateway (192.168.20.1) -> Synology NAS eth0 (192.168.20.2)
Synology NAS eth1 (192.168.21.1) -> Netgear Switch (192.168.21.2) -> RPi
ISP Gateway - Static IP Lease

I used the Gateway's web UI (Advanced -> Local Network -> LAN) to configure a static IP lease for the NAS (eth0):

Gateway-DHCP-static-lease

You can use the following command to obtain a MAC address:

ethtool -P eth0
Synology DiskStation Manager (DSM) - Static IP

I used the Synology DiskStation Manager (DSM) to configure static IP's for the NAS's ethernet interfaces:

network-interface

Synology DiskStation Manager (DSM) - DHCP Server

I used the Synology DiskStation Manager (DSM) to configure the NAS's DHCP Server:

NAS-DHCP-Server

I also used the NAS's DHCP Server to configure a static IP lease for my Netgear switch (192.168.21.2).

I used the Netgear switch's web UI to configure a static IP (192.168.21.2):

Switch-static-ip

ISP Gateway - Static Routes

I used the Gateway's web UI (Advanced -> Routing) to configure a static route to the subnet (192.168.21.0/24):

static-route

Note: The static route 'Gateway' setting is for the next hop (i.e., if the gateway's IP address is: 192.168.20.1 the next hop is 192.168.20.2).

Ping a device in the subnet

If you can't ping a device in the subnet you may need to use the sysctl command to enable IP forwarding (on the NAS).

sudo sysctl -w net.ipv4.ip_forward=1

To make the change persistent, you need to edit the /etc/sysctl.conf file:

sudo nano /etc/sysctl.conf

And add the following line to the bottom of the file:

net.ipv4.ip_forward = 1
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