Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
986 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C92×C43 | C32 |
| commutator | C3 | C33×C9×C43 |
| Frattini, cosocle | C32 | C34×C43 |
| socle | C32×C43 | C34 |
| prime radical | C3×H(3,𝔽3)×C43 | C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C92×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×3−1+2×C43 | C3 | semidirect |
| 4. C43×#6887 | C3 | semidirect |
| 5. C3×C92×C43 | C3 | semidirect |
| 6. C43×#737 | C9 | direct (N × H) |
| 17. 3−1+2×C43 | C3×C9 | semidirect |
| 20. C3×C9×C43 | C3×C9 | semidirect |
| 25. C9×#737 | C43 | direct (N × H) |
| 32. C9×C43 | #737 | direct (N × H) |
| 34. C9×3−1+2 | C3×C43 | semidirect |
| 36. #6887 | C3×C43 | semidirect |
| 37. C3×C92 | C3×C43 | semidirect |
| 41. #737 | C9×C43 | direct (N × H) |
| 51. C43 | C9×#737 | direct (N × H) |
| 53. 3−1+2 | C3×C9×C43 | semidirect |
| 56. C3×C9 | C3×C9×C43 | semidirect |
| 67. C9 | C43×#737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×#737 | 3 |
| C9×3−1+2×C43 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C43×#6887 | 3 |
| C3×C92×C43 | 3 |
| C9×#737 | 43 |