Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
960 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 268 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. C3×#16812525 | C3 | semidirect |
| 2. #737×C43⋊C3 | C3 | semidirect |
| 3. #23782906 | C3 | semidirect |
| 4. #23782903 | C3 | semidirect |
| 5. #23782901 | C3 | semidirect |
| 6. #23782897 | C3 | semidirect |
| 7. #23782893 | C3 | semidirect |
| 8. #23782889 | C3 | semidirect |
| 9. #23782884 | C3 | semidirect |
| 10. #23782879 | C3 | semidirect |
| 11. #23782877 | C3 | semidirect |
| 12. #23782874 | C3 | semidirect |
| 13. C43×#6908 | C3 | semidirect |
| 15. #16812526 | C32 | semidirect |
| 19. #16812525 | C32 | semidirect |
| 20. #16812524 | C32 | semidirect |
| 21. C3×#11923958 | C32 | semidirect |
| 23. C3×#11923957 | C32 | semidirect |
| 25. C3×#11923956 | C32 | semidirect |
| 32. C3×C9×C43⋊C3 | C32 | semidirect |
| 33. #16812515 | C32 | semidirect |
| 34. #16812514 | C32 | semidirect |
| 37. #16812511 | C32 | semidirect |
| 38. #16812510 | C32 | semidirect |
| 39. #16812509 | C32 | semidirect |
| 40. #16812508 | C32 | semidirect |
| 41. #16812507 | C32 | semidirect |
| 42. #16812506 | C32 | semidirect |
| 43. C43×#737 | C32 | semidirect |
| 44. C32×C9×C43 | C32 | semidirect |
| 45. C43×#733 | C32 | semidirect |
| 47. C43×#731 | C32 | semidirect |
| 48. C43×AΣL(1,𝔽27) | C32 | semidirect |
| 121. #6908 | C43⋊C3 | semidirect |
| 136. #737 | C3×C43⋊C3 | semidirect |
| 149. C32×C9 | C3×C43⋊C3 | semidirect |
| 152. #733 | C3×C43⋊C3 | semidirect |
| 159. #731 | C3×C43⋊C3 | semidirect |
| 163. AΣL(1,𝔽27) | C3×C43⋊C3 | semidirect |
| 164. C43 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #737×C43⋊C3 | 3 |
| #23782906 | 3 |
| #23782903 | 3 |
| #23782901 | 3 |
| #23782897 | 3 |
| #23782893 | 3 |
| #23782889 | 3 |
| #23782884 | 3 |
| #23782879 | 3 |
| #23782877 | 3 |
| #23782874 | 3 |
| C43×#6908 | 3 |
| #10624929 | 43 |