Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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. #23782905 | C3 | semidirect |
| 2. #23782845 | C3 | semidirect |
| 3. #23782769 | C3 | semidirect |
| 4. #23782768 | C3 | semidirect |
| 5. #23782756 | C3 | semidirect |
| 6. #23782755 | C3 | semidirect |
| 7. #23782750 | C3 | semidirect |
| 8. #23782745 | C3 | semidirect |
| 9. C43×#6911 | C3 | semidirect |
| 12. #16812515 | C32 | semidirect |
| 13. #16812515 | C32 | semidirect |
| 14. #16812513 | C32 | semidirect |
| 17. #16812500 | C32 | semidirect |
| 18. #16812499 | C32 | semidirect |
| 20. C9×C43⋊C9 | C32 | semidirect |
| 60. #6911 | C43⋊C3 | semidirect |
| 90. C43 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782905 | 3 |
| #23782845 | 3 |
| #23782769 | 3 |
| #23782768 | 3 |
| #23782756 | 3 |
| #23782755 | 3 |
| #23782750 | 3 |
| #23782745 | 3 |
| C43×#6911 | 3 |
| #10624851 | 43 |