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
36T22678 $C_3^8.(C_3\times Q_8)$ $157464$ $1$ ✓ $1$ $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $C_6\times C_2$ 36T22678 x 53, 36T22684 x 108
36T22684 $C_3^8.(C_3\times Q_8)$ $157464$ $1$ ✓ $1$ $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $C_6\times C_2$ 36T22678 x 54, 36T22684 x 107
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