Subneting is the process of breaking up IP address networks into smaller networks. It is typically used in the context of an ISP providing a company a /16 (for example), which is 65536~ IP Addresses, and that company breaking up those 65k IP addresses into smaller groups for more efficient deployment in their network.
Segmentation is the concept of breaking up one larger network into multiple smaller network. It is often associated with VLANs, but doesn't require them. BUT, each new network does require its own IP address range, and therefore also involves the process of Subneting described above.
Segregation can probably mean different things to different shops, but I've always taken it to mean the concept of placing servers/hosts with different security requirements in different network "zones" so you can apply security policies to traffic flowing to and in between them.
For example, traffic flowing to your web server will be filtered differently than traffic flowing to your database server. As such, it is wise to put your web server in a different network than your database server, and also ideally separate those networks with some sort of Firewall or security device.
Segregation will involve creating different/isolated networks, which might involve Segmentation, which will therefore also involve Subnetting.