Subgraph classification is an emerging field in graph representation learning where the task is to classify a group of nodes (i.e., a subgraph) within a graph. Subgraph classification has applications such as predicting the cellular function of a group of proteins or identifying rare diseases given a collection of phenotypes. Graph neural networks (GNNs) are the de facto solution for node, link, and graph-level tasks but fail to perform well on subgraph classification tasks. Even GNNs tailored for graph classification are not directly transferable to subgraph classification as they ignore the external topology of the subgraph, thus failing to capture how the subgraph is located within the larger graph. The current state-of-the-art models for subgraph classification address this shortcoming through either labeling tricks or multiple message-passing channels, both of which impose a computation burden and are not scalable to large graphs. To address the scalability issue while maintaining generalization, we propose Stochastic Subgraph Neighborhood Pooling (SSNP), which jointly aggregates the subgraph and its neighborhood (i.e., external topology) information without any computationally expensive operations such as labeling tricks. To improve scalability and generalization further, we also propose a simple data augmentation pre-processing step for SSNP that creates multiple sparse views of the subgraph neighborhood. We show that our model is more expressive than GNNs without labeling tricks. Our extensive experiments demonstrate that our models outperform current state-of-the-art methods (with a margin of up to 2%) while being up to 3X faster in training.