Why can't i play LAN worlds on minecraft when connected to my verizon modem/router?

Why can't i play LAN worlds on minecraft when connected to my verizon modem/router?

Added (1). -in other words, when the computers within the house are connected directly to the verizon provided router, can't join each other in lan worlds. But if i hang another router off of the verizon router, we can play no problem if all connected to that other router.

All the computers need to be on the same subnet for the LAN, so if you aren't connected to the Verizon router when you do play, what are those computers connected to if not the modem/router?