Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1082 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 280 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. C32×#11923957 | C3 | semidirect |
| 3. #23782807 | C3 | semidirect |
| 4. #23782804 | C3 | semidirect |
| 5. #23782802 | C3 | semidirect |
| 6. #23782802 | C3 | semidirect |
| 7. #23782801 | C3 | semidirect |
| 8. #23782800 | C3 | semidirect |
| 9. #23782796 | C3 | semidirect |
| 11. #23782783 | C3 | semidirect |
| 12. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 13. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 16. C3×#11923958 | C32 | semidirect |
| 22. C3×#11923957 | C32 | semidirect |
| 24. C3×#11923956 | C32 | semidirect |
| 30. C3×C9×C43⋊C3 | C32 | semidirect |
| 33. C32⋊(C43⋊C9) | C32 | semidirect |
| 36. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 37. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 38. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 41. C32×C9×C43 | C32 | semidirect |
| 44. C43×C32⋊C9 | C32 | semidirect |
| 56. #11923957 | H(3,𝔽3) | semidirect |
| 84. C32×C43 | #737 | semidirect |
| 116. C9×H(3,𝔽3) | C43⋊C3 | semidirect |
| 145. C32×C9 | C3×C43⋊C3 | semidirect |
| 156. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 157. C43 | #10624896 | semidirect |
| 207. C32 | #16812525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| C32×#11923957 | 3 |
| #23782807 | 3 |
| #23782804 | 3 |
| #23782802 | 3 |
| #23782801 | 3 |
| #23782800 | 3 |
| #23782796 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| #23782783 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| #10624896 | 43 |