Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
596 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 250 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. #23782845 | C3 | semidirect |
| 2. #23782836 | C3 | semidirect |
| 3. #23782835 | C3 | semidirect |
| 4. #23782833 | C3 | semidirect |
| 5. #23782832 | C3 | semidirect |
| 6. #23782831 | C3 | semidirect |
| 7. #23782830 | C3 | semidirect |
| 9. C43×#6900 | C3 | semidirect |
| 12. #16812500 | C32 | semidirect |
| 13. #16812499 | C32 | semidirect |
| 14. (C43⋊C9)⋊C9 | C32 | semidirect |
| 15. (C43⋊C9)⋊C9 | C32 | semidirect |
| 16. (C43⋊C9)⋊C9 | C32 | semidirect |
| 17. (C43⋊C9)⋊C9 | C32 | semidirect |
| 24. C9×C43⋊C9 | C32 | semidirect |
| 26. C43×C9⋊C9 | C32 | semidirect |
| 27. C92×C43 | C32 | semidirect |
| 53. #6900 | C43⋊C3 | semidirect |
| 75. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 83. C92 | C3×C43⋊C3 | semidirect |
| 84. C43 | #10624912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782845 | 3 |
| #23782836 | 3 |
| #23782835 | 3 |
| #23782833 | 3 |
| #23782832 | 3 |
| #23782831 | 3 |
| #23782830 | 3 |
| #23782795 | 3 |
| C43×#6900 | 3 |
| #10624912 | 43 |