Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
740 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 740 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 |
|---|---|---|
| 2. #23782837 | C3 | semidirect |
| 3. #23782823 | C3 | semidirect |
| 4. #23782818 | C3 | semidirect |
| 5. #23782817 | C3 | semidirect |
| 6. #23782816 | C3 | semidirect |
| 7. #23782815 | C3 | semidirect |
| 10. #23782792 | C3 | semidirect |
| 11. C9×#11923958 | C3 | semidirect |
| 22. #16812500 | C32 | semidirect |
| 23. #16812499 | 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 |
| 36. C9×C43⋊C9 | C32 | semidirect |
| 50. #11923958 | 3−1+2 | semidirect |
| 147. C43 | #10624899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| #23782837 | 3 |
| #23782823 | 3 |
| #23782818 | 3 |
| #23782817 | 3 |
| #23782816 | 3 |
| #23782815 | 3 |
| #23782798 | 3 |
| #23782792 | 3 |
| C9×#11923958 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624899 | 43 |