Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
620 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 256 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. #23782833 | C3 | semidirect |
| 2. #23782832 | C3 | semidirect |
| 3. #23782831 | C3 | semidirect |
| 4. #23782830 | C3 | semidirect |
| 5. #23782826 | C3 | semidirect |
| 6. #23782825 | C3 | semidirect |
| 7. #23782818 | C3 | semidirect |
| 8. #23782817 | C3 | semidirect |
| 9. #23782812 | C3 | semidirect |
| 13. C9×#11923958 | C3 | semidirect |
| 15. C9×3−1+2×C43 | C3 | semidirect |
| 21. #16812500 | C32 | semidirect |
| 22. #16812499 | C32 | semidirect |
| 23. (C43⋊C9)⋊C9 | C32 | semidirect |
| 24. (C43⋊C9)⋊C9 | C32 | semidirect |
| 25. (C43⋊C9)⋊C9 | C32 | semidirect |
| 26. (C43⋊C9)⋊C9 | C32 | semidirect |
| 27. (C43⋊C9)⋊C9 | C32 | semidirect |
| 28. (C43⋊C9)⋊C9 | C32 | semidirect |
| 29. (C43⋊C9)⋊C9 | C32 | semidirect |
| 30. (C43⋊C9)⋊C9 | C32 | semidirect |
| 31. (C43⋊C9)⋊C9 | C32 | semidirect |
| 47. C9×C43⋊C9 | C32 | semidirect |
| 50. C43×C9⋊C9 | C32 | semidirect |
| 53. C92×C43 | C32 | semidirect |
| 122. C9×3−1+2 | C43⋊C3 | semidirect |
| 150. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 169. C92 | C3×C43⋊C3 | semidirect |
| 170. C43 | #10624889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782833 | 3 |
| #23782832 | 3 |
| #23782831 | 3 |
| #23782830 | 3 |
| #23782826 | 3 |
| #23782825 | 3 |
| #23782818 | 3 |
| #23782817 | 3 |
| #23782812 | 3 |
| #23782797 | 3 |
| #23782796 | 3 |
| #23782795 | 3 |
| C9×#11923958 | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C9×3−1+2×C43 | 3 |
| #10624889 | 43 |