Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 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. #23782924 | C3 | semidirect |
| 2. #23782923 | C3 | semidirect |
| 3. C3×#16812524 | C3 | semidirect |
| 4. #23782898 | C3 | semidirect |
| 5. #23782897 | C3 | semidirect |
| 6. #23782895 | C3 | semidirect |
| 7. #23782891 | C3 | semidirect |
| 8. #23782882 | C3 | semidirect |
| 9. #23782873 | C3 | semidirect |
| 10. C3×#16812511 | C3 | semidirect |
| 11. C3×#16812509 | C3 | semidirect |
| 12. C43×#6909 | C3 | semidirect |
| 14. #16812526 | C32 | semidirect |
| 19. #16812524 | C32 | semidirect |
| 25. C3×#11923958 | C32 | semidirect |
| 26. C3×#11923958 | C32 | semidirect |
| 30. C32×C43⋊C9 | C32 | semidirect |
| 31. #16812514 | C32 | semidirect |
| 33. #16812511 | C32 | semidirect |
| 34. #16812511 | C32 | semidirect |
| 35. #16812511 | C32 | semidirect |
| 36. #16812509 | C32 | semidirect |
| 37. #16812509 | C32 | semidirect |
| 38. #16812509 | C32 | semidirect |
| 39. #16812507 | C32 | semidirect |
| 43. C43×AΣL(1,𝔽27) | C32 | semidirect |
| 113. #6909 | C43⋊C3 | semidirect |
| 154. AΣL(1,𝔽27) | C3×C43⋊C3 | semidirect |
| 155. C43 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782924 | 3 |
| #23782923 | 3 |
| C3×#16812524 | 3 |
| #23782898 | 3 |
| #23782897 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782882 | 3 |
| #23782873 | 3 |
| C3×#16812511 | 3 |
| C3×#16812509 | 3 |
| C43×#6909 | 3 |
| #10624935 | 43 |