Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
980 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 980 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 4. #23782904 | C3 | semidirect |
| 5. #23782903 | C3 | semidirect |
| 6. #23782895 | C3 | semidirect |
| 7. #23782891 | C3 | semidirect |
| 8. #23782887 | C3 | semidirect |
| 9. #23782876 | C3 | semidirect |
| 10. C3×#16812508 | C3 | semidirect |
| 11. C3×#16812506 | C3 | semidirect |
| 12. C43×#6910 | C3 | semidirect |
| 15. #16812526 | C32 | semidirect |
| 18. #16812524 | C32 | semidirect |
| 24. C3×#11923957 | C32 | semidirect |
| 25. C3×#11923956 | C32 | semidirect |
| 30. C3×C9×C43⋊C3 | C32 | semidirect |
| 31. #16812514 | C32 | semidirect |
| 32. #16812512 | C32 | semidirect |
| 33. #16812510 | C32 | semidirect |
| 34. #16812508 | C32 | semidirect |
| 35. #16812508 | C32 | semidirect |
| 36. #16812508 | C32 | semidirect |
| 37. #16812506 | C32 | semidirect |
| 38. #16812506 | C32 | semidirect |
| 39. #16812506 | C32 | semidirect |
| 43. C43×#731 | C32 | semidirect |
| 118. #6910 | C43⋊C3 | semidirect |
| 155. #731 | C3×C43⋊C3 | semidirect |
| 162. C43 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782924 | 3 |
| #23782923 | 3 |
| C3×3−1+2×C43⋊C3 | 3 |
| #23782904 | 3 |
| #23782903 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782887 | 3 |
| #23782876 | 3 |
| C3×#16812508 | 3 |
| C3×#16812506 | 3 |
| C43×#6910 | 3 |
| #10624934 | 43 |