Steiner Triple Systems of Order 21 with Subsystems

The smallest open case for classifying Steiner triple systems is order 21. A Steiner triple system of order 21, an STS, can have subsystems of orders 7 and 9, and it is known that there are 12,661,527,336 isomorphism classes of STSs with sub-STSs. Here, the classification of STSs with subsystems is completed by settling the case of STSs with sub-STSs. There are 116,635,963,205,551 isomorphism classes of such systems. An estimation of the number of isomorphism classes of STSs is given