Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
290 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 5. #23782708 | C3 | semidirect |
| 6. #23782707 | C3 | semidirect |
| 7. #23782707 | C3 | semidirect |
| 8. #23782706 | C3 | semidirect |
| 9. #23782706 | C3 | semidirect |
| 10. C9×C43⋊C27 | C3 | semidirect |
| 11. C27×C43⋊C9 | C3 | semidirect |
| 12. C27×C43⋊C9 | C3 | semidirect |
| 13. C43×#6864 | C3 | semidirect |
| 15. #16812504 | C9 | semidirect |
| 16. #16812503 | C9 | semidirect |
| 23. C27×C43⋊C3 | C9 | semidirect |
| 70. #6864 | C43⋊C3 | semidirect |
| 95. C43 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812504 | 3 |
| C3×#16812503 | 3 |
| C3×C27×C43⋊C3 | 3 |
| #23782780 | 3 |
| #23782708 | 3 |
| #23782707 | 3 |
| #23782706 | 3 |
| C9×C43⋊C27 | 3 |
| C27×C43⋊C9 | 3 |
| C43×#6864 | 3 |
| #10624681 | 43 |