Cannot ping from inside a VLAN to anywhere outside itself

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Hello everyone

I've created, with virtualbox, a virtual network on my computer.

First, here is a link to a detailed diagram of my LAN.

The servers are on a 192.168.10.0/24 network, and one of them, 192.168.10.1 behaves as a router and has a bridge connection to my computer. It has the address 192.168.1.45 while my PC has the address 192.168.1.20. The switch is virtual, handled by virtualbox, which also handles the bridge connection.

The issue is that when I try a ping from 192.168.10.6 to 192.168.1.1 - the livebox, 8.8.8.8 or even 192.168.1.20, it doesn't get any answer, while tcpdump says that the requests are sent.

It's the same with every VM, but everything is fine when I try from 192.168.10.1...

The farest IP I can reach with a ping is 192.168.1.45.

When I try to ping 192.168.1.20 and do a tcpdump on 192.168.1.20, it shows that 192.168.1.20 receives the request, but doesn't send any answer back :

listening on enp3s0, link-type EN10MB (Ethernet), capture size 262144 bytes
22:26:34.676988 IP 192.168.10.4 > 192.168.1.20: ICMP echo request, id 765, seq 1, length 64
22:26:35.685914 IP 192.168.10.4 > 192.168.1.20: ICMP echo request, id 765, seq 2, length 64
22:26:36.686520 IP 192.168.10.4 > 192.168.1.20: ICMP echo request, id 765, seq 3, length 64
22:26:37.687863 IP 192.168.10.4 > 192.168.1.20: ICMP echo request, id 765, seq 4, length 64

And :

• So that the network can be reached from internet, since we cannot modify the routing table of liveboxes, I made a DMZ at 192.168.1.45.
• So that the servers can be reached when the DMZ is reached, I use socat on the DHCP server. Here's an example : socat TCP4-LISTEN:80,fork TCP4:192.168.10.6:80.
• I'm a beginner at networking, so tell me everything you think you should tell.

Thank you for helping !