Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1064 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 271 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #737×C43⋊C3 | C3 | semidirect |
| 2. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. #23782878 | C3 | semidirect |
| 4. #23782877 | C3 | semidirect |
| 5. #23782876 | C3 | semidirect |
| 6. #23782875 | C3 | semidirect |
| 7. #23782874 | C3 | semidirect |
| 8. #23782873 | C3 | semidirect |
| 9. #733×C43⋊C3 | C3 | semidirect |
| 10. #732×C43⋊C3 | C3 | semidirect |
| 11. #731×C43⋊C3 | C3 | semidirect |
| 12. AΣL(1,𝔽27)×C43⋊C3 | C3 | semidirect |
| 13. C43×#6908 | C3 | semidirect |
| 16. #16812526 | C32 | semidirect |
| 18. #16812525 | C32 | semidirect |
| 19. #16812524 | C32 | semidirect |
| 23. C32×C43⋊C9 | C32 | semidirect |
| 32. C3×C9×C43⋊C3 | C32 | semidirect |
| 33. C3×C9×C43⋊C3 | C32 | semidirect |
| 34. C3×C9×C43⋊C3 | C32 | semidirect |
| 35. #16812515 | C32 | semidirect |
| 36. #16812514 | C32 | semidirect |
| 37. #16812513 | C32 | semidirect |
| 38. #16812512 | C32 | semidirect |
| 39. #16812511 | C32 | semidirect |
| 40. #16812510 | C32 | semidirect |
| 41. #16812509 | C32 | semidirect |
| 42. #16812508 | C32 | semidirect |
| 43. #16812507 | C32 | semidirect |
| 44. #16812506 | C32 | semidirect |
| 45. C43×#737 | C32 | semidirect |
| 46. C32×C9×C43 | C32 | semidirect |
| 47. C43×#733 | C32 | semidirect |
| 48. C43×#732 | C32 | semidirect |
| 49. C43×#731 | C32 | semidirect |
| 50. C43×AΣL(1,𝔽27) | C32 | semidirect |
| 132. #6908 | C43⋊C3 | direct (N × H) |
| 144. C43⋊C3 | #6908 | direct (N × H) |
| 151. #737 | C3×C43⋊C3 | semidirect |
| 167. C32×C9 | C3×C43⋊C3 | semidirect |
| 170. #733 | C3×C43⋊C3 | semidirect |
| 173. #732 | C3×C43⋊C3 | semidirect |
| 177. #731 | C3×C43⋊C3 | semidirect |
| 181. AΣL(1,𝔽27) | C3×C43⋊C3 | semidirect |
| 182. C43 | C3×#6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| #23782878 | 3 |
| #23782877 | 3 |
| #23782876 | 3 |
| #23782875 | 3 |
| #23782874 | 3 |
| #23782873 | 3 |
| #733×C43⋊C3 | 3 |
| #732×C43⋊C3 | 3 |
| #731×C43⋊C3 | 3 |
| AΣL(1,𝔽27)×C43⋊C3 | 3 |
| C43×#6908 | 3 |
| C3×#6908 | 43 |