Ontology search interfaces can benefit from the latest information retrieval advances. This paper introduces a Conjunctive Ontology Browser and Explorer (COBE) for searching and exploring SNOMED CT concepts and visualizing SNOMED CT fragments. COBE combines navigational exploration (NE) with direct lookup (DL) as two complementary modes for finding specific SNOMED CT concepts. The NE mode allows a user to interactively and incrementally narrow down (hence conjunctive) the search space by adding word stems, one at a time. Such word stems serve as attribute constraints, or "attributes" in Formal Concept Analysis, which allows the user to navigate to specific SNOMED CT concept clusters. The DL mode represents the common search mechanism by using a collection of key words, as well as concept identifiers. With respect to the DL mode, evaluation against manually created reference standard showed that COBE attains an example-based precision of 0.958, recall of 0.917, and F1 measure of 0.875. With respect to the NE mode, COBE leverages 28,371 concepts in non-lattice fragments to construct the stem cloud. With merely 9.37% of the total SNOMED CT stem cloud, our navigational exploration mode covers 98.97% of the entire concept collection.