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×#16812526 | C3 | semidirect |
| 2. C3×#16812524 | C3 | semidirect |
| 3. C3×#16812524 | C3 | semidirect |
| 4. #23782898 | C3 | semidirect |
| 5. #23782897 | C3 | semidirect |
| 6. #23782895 | C3 | semidirect |
| 7. #23782891 | C3 | semidirect |
| 8. #23782888 | C3 | semidirect |
| 9. #23782886 | C3 | semidirect |
| 10. #23782882 | C3 | semidirect |
| 11. #23782873 | C3 | semidirect |
| 12. C43×#6909 | C3 | semidirect |
| 19. #16812526 | C32 | semidirect |
| 20. #16812526 | C32 | semidirect |
| 21. #16812526 | C32 | semidirect |
| 30. #16812524 | C32 | semidirect |
| 31. #16812524 | C32 | semidirect |
| 32. #16812524 | C32 | semidirect |
| 38. C3×#11923958 | C32 | semidirect |
| 39. C3×#11923958 | C32 | semidirect |
| 45. C32×C43⋊C9 | C32 | semidirect |
| 47. #16812514 | C32 | semidirect |
| 49. #16812511 | C32 | semidirect |
| 50. #16812509 | C32 | semidirect |
| 51. #16812507 | C32 | semidirect |
| 55. C43×AΣL(1,𝔽27) | C32 | semidirect |
| 145. #6909 | C43⋊C3 | semidirect |
| 196. AΣL(1,𝔽27) | C3×C43⋊C3 | semidirect |
| 197. C43 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812526 | 3 |
| C3×#16812524 | 3 |
| #23782898 | 3 |
| #23782897 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782888 | 3 |
| #23782886 | 3 |
| #23782882 | 3 |
| #23782873 | 3 |
| C43×#6909 | 3 |
| #10624929 | 43 |