Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
788 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 262 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. #23782807 | C3 | semidirect |
| 2. #23782805 | C3 | semidirect |
| 3. #23782804 | C3 | semidirect |
| 4. #23782803 | C3 | semidirect |
| 5. #23782802 | C3 | semidirect |
| 6. #23782801 | C3 | semidirect |
| 7. #23782798 | C3 | semidirect |
| 9. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 10. #23782783 | C3 | semidirect |
| 11. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 12. C3×C43×C32⋊C9 | C3 | semidirect |
| 14. C3×#11923957 | C32 | semidirect |
| 15. C3×#11923956 | C32 | semidirect |
| 21. C3×C9×C43⋊C3 | C32 | semidirect |
| 30. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 31. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 32. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 33. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 34. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 35. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 110. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 150. C43 | #10624905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782807 | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782801 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782783 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624905 | 43 |