Network layer Internet topology consists of a set of routers connected to each other through subnets. Recently, there has been a significant interest in studying topological characteristics of subnets in addition to routers in the Internet. However, given the size of the Internet, constructing complete subnet level topology maps is neither practical nor economical. A viable solution, then, is to sample subnets in the target domain and estimate their global characteristics. In this study, we propose a sampling framework for subnets; derive proper estimators for various subnet characteristics including total number of subnets, subnet prefix length distribution, mean subnet degree, and IP address utilization; and analyze the theoretical and empirical aspects of these estimators.