Database
[{_id:ObjectId("10a5531cd6186f39b42d4344"),type:"A",groupBy:"1"},{_id:ObjectId("20a5331cd6186f39b42d4344"),type:"B",groupBy:"1"},{_id:ObjectId("30a5531cd6186f39b42d4344"),type:"A",groupBy:"2"},{_id:ObjectId("40a5533cd6196f39b42d4344"),type:"B",groupBy:"2"}]
Query
db.collection.aggregate([{"$group":{"_id":"$groupBy","typeA":{"$push":{"$cond":[{"$eq":["$type","A"]},"$$ROOT","$$REMOVE"]}},"typeB":{"$push":{"$cond":[{"type":"B"},"$$ROOT","$$REMOVE"]}}}}])