Where is the gateway IP address of the VLAN?
We know the Switch can divide the VLAN, such as it can divide the 103.19.1.0/24 to 103.19.1.0/25 and 103.19.1.128/25.
if the 103.19.1.0/25's gateway IP address is 103.19.1.1, so whether does the gateway's location?
Is it in the Switch?
The gateway is, by definition, on a router.
This router can be the switch itself, if it is a layer 3 switch. A layer 3 switch is indeed a device that incorporate two functions: switch and router.
It can be an external router, and in this case usually, there's a link between the switch(es) and the router that carry several VLANs, called a trunk (except in some HP switches where the term trunk refer to link bonding instead).
You will find some information on this page: https://www.practicalnetworking.net/stand-alone/vlans/
In router
If inter-Vlan configuration is done in router then gateway of router will be in router
In layer3 devices
If Switch virtual interfàce (SVI) with Vlan are configured in layer3 switch then Vlan gateway willl be in layer3 switch
In firewall
If inter vlan routing is configured on firewall with subinterface using Vlan. then Vlan gateway will be in firewall.
We know the Switch can divide the VLAN,
Yes, a managed switch can separate its traffic into multiple VLANs. Each VLAN forms a separate broadcast domain on the data link layer (L2).
such as it can divide the 103.19.1.0/24 to 103.19.1.0/25 and 103.19.1.128/25.
Careful not to mix L2 and L3 (network layer). While VLANs separate L2 traffic they don't use IP addresses nor do L2 switches.
Subnetting is a layer 3 mechanism - while it is most often closely related to VLANs, both are distinct aspects: nodes in different VLANs cannot communicate with each other by definition (on L2), but those nodes can use the network layer to communicate across a gateway/router. That in turn requires proper addressing which can be accomplished using subnetting.
if the 103.19.1.0/25's gateway IP address is 103.19.1.1, so whether does the gateway's location?
The gateway can be part of a layer-3 switch ("switch virtual interface" on Cisco) or it can be attached externally to the switch. Of course, an external gateway needs to be connected to each VLAN it's supposed to provide gateway services to. Those connections can be physical - one link for each VLAN, or logical - a single physical link with logical subinterfaces and trunked VLANs.
To actually find a gateway configured by someone else, you need to know its MAC address (by ARP) and locate that MAC address in the switch's source address table.
