Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
198 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 88 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. #23782739 | C3 | semidirect |
| 6. #23782739 | C3 | semidirect |
| 7. #23782738 | C3 | semidirect |
| 8. #23782738 | C3 | semidirect |
| 9. #23782737 | C3 | semidirect |
| 10. #23782736 | C3 | semidirect |
| 11. #23782735 | C3 | semidirect |
| 12. #23782735 | C3 | semidirect |
| 13. C43×#6875 | C3 | semidirect |
| 23. #16812504 | C9 | semidirect |
| 26. #16812503 | C9 | semidirect |
| 29. C27×C43⋊C3 | C9 | semidirect |
| 94. #6875 | C43⋊C3 | semidirect |
| 125. C43 | #10624709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27⋊C3×C43⋊C3 | 3 |
| #23782781 | 3 |
| #23782739 | 3 |
| #23782738 | 3 |
| #23782737 | 3 |
| #23782736 | 3 |
| #23782735 | 3 |
| C43×#6875 | 3 |
| #10624709 | 43 |