Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 764 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. #23782807 | C3 | semidirect |
| 2. #23782805 | C3 | semidirect |
| 3. #23782804 | C3 | semidirect |
| 4. #23782801 | C3 | semidirect |
| 5. #23782799 | C3 | semidirect |
| 6. #23782798 | C3 | semidirect |
| 8. #23782783 | C3 | semidirect |
| 9. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 10. C43×#6891 | C3 | semidirect |
| 12. C3×#11923957 | C32 | semidirect |
| 13. C3×#11923956 | C32 | semidirect |
| 21. C3×C9×C43⋊C3 | C32 | semidirect |
| 28. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 29. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 30. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 96. #6891 | C43⋊C3 | semidirect |
| 134. C43 | #10624888 | 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 |
| #23782801 | 3 |
| #23782799 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| #23782783 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C43×#6891 | 3 |
| #10624888 | 43 |