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. #23782803 | C3 | semidirect |
| 3. #23782802 | C3 | semidirect |
| 4. #23782801 | C3 | semidirect |
| 5. #23782798 | C3 | semidirect |
| 7. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 8. C3×C43×C32⋊C9 | C3 | semidirect |
| 10. C3×#11923957 | C32 | semidirect |
| 11. C3×#11923956 | C32 | semidirect |
| 15. C3×C9×C43⋊C3 | C32 | semidirect |
| 19. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 20. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 21. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 76. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 103. C43 | #10624888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782807 | 3 |
| #23782803 | 3 |
| #23782802 | 3 |
| #23782801 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624888 | 43 |