The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
$\#\Aut(F/K)$ Transitivity
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Results (displaying both matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
18T235 $C_9^2:C_{12}$ $972$ $-1$ ✓ $1$ $C_2$, $C_3^2:C_4$ 18T235 x 5, 36T1495 x 6
36T1495 $C_9^2:C_{12}$ $972$ $-1$ ✓ $6$ $C_2$, $C_4$, $C_3^2:C_4$, $(C_3\times C_3):C_4$, $C_9^2:C_{12}$ 18T235 x 6, 36T1495 x 5
  displayed columns for results