Click within the Deployments tab in the Administrative Console and drill-down into the war file to see the artifacts:

There is currently no way to view artifacts within a deployable file (WAR, etc.) within the Administrative Console. It is incredibly useful to an Administrative/Ops type to be able to drill-down into the deployable file and view the specific artifacts. This would assist in troubleshooting and diagnosing issues. At the same time, the user within the Administrative Console should be able to click the context and get to the deployed application (if it is a web-based context like a WAR).