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