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The database current contains $512{,}613$ groups, including all transitive subgroups of $S_n$ (up to conjugacy) for $n \le 47$ and $n \ne 32$. Here are some further statistics.

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By degree: 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47 
By type: odd  even  cyclic  noncyclic  solvable  nonsolvable  primitive  imprimitive 
By group: $S_3$  $D_4$  $A_4$  $S_4$  $A_5$  $S_5$  $\GL(3,2)$  $A_6$  $\PSL(2,8)$  $\PSL(2,11)$  $\PSL(2,13)$  $\PSL(3,3)$  $\PSU(3,3)$  $\PSp(4,3)$  $M_{11}$  $M_{12}$  $\cdots$
Some interesting Galois groups or a random Galois group

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e.g. 8T14