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

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Results (displaying both matches)

  displayed columns for results
Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
11T5 $\PSL(2,11)$ $660$ $1$ $1$ 11T5, 12T179
12T179 $\PSL(2,11)$ $660$ $1$ $1$ 11T5 x 2
  displayed columns for results