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×#16812526 | C3 | semidirect |
| 3. C3×#16812524 | C3 | semidirect |
| 4. #23782904 | C3 | semidirect |
| 5. #23782903 | C3 | semidirect |
| 6. #23782895 | C3 | semidirect |
| 7. #23782891 | C3 | semidirect |
| 8. #23782887 | C3 | semidirect |
| 9. #23782883 | C3 | semidirect |
| 10. #23782881 | C3 | semidirect |
| 11. #23782876 | C3 | semidirect |
| 12. C43×#6910 | C3 | semidirect |
| 24. #16812526 | C32 | semidirect |
| 25. #16812526 | C32 | semidirect |
| 26. #16812526 | C32 | semidirect |
| 30. #16812524 | C32 | semidirect |
| 31. #16812524 | C32 | semidirect |
| 32. #16812524 | C32 | semidirect |
| 38. C3×#11923957 | C32 | semidirect |
| 40. C3×#11923956 | C32 | semidirect |
| 46. C3×C9×C43⋊C3 | C32 | semidirect |
| 47. #16812514 | C32 | semidirect |
| 49. #16812510 | C32 | semidirect |
| 50. #16812508 | C32 | semidirect |
| 51. #16812506 | C32 | semidirect |
| 55. C43×#731 | C32 | semidirect |
| 143. #6910 | C43⋊C3 | semidirect |
| 194. #731 | 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 |
| #23782904 | 3 |
| #23782903 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782887 | 3 |
| #23782883 | 3 |
| #23782881 | 3 |
| #23782876 | 3 |
| C43×#6910 | 3 |
| #10624929 | 43 |