Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
432 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 61 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. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. #23782817 | C3 | semidirect |
| 4. #23782812 | C3 | semidirect |
| 5. #23782805 | C3 | semidirect |
| 6. #23782724 | C3 | semidirect |
| 7. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 8. #23782722 | C3 | semidirect |
| 9. #23782721 | C3 | semidirect |
| 10. #23782719 | C3 | semidirect |
| 11. #23782711 | C3 | semidirect |
| 12. #23782711 | C3 | semidirect |
| 13. C43×3−1+2⋊C9 | C3 | semidirect |
| 48. C32×C43⋊C3 | 3−1+2 | semidirect |
| 110. C43⋊C9 | AΣL(1,𝔽27) | semidirect |
| 119. 3−1+2⋊C9 | C43⋊C3 | semidirect |
| 160. C43 | #10624784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C3×#16812508 | 3 |
| #23782817 | 3 |
| #23782812 | 3 |
| #23782805 | 3 |
| #23782724 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782722 | 3 |
| #23782721 | 3 |
| #23782719 | 3 |
| #23782711 | 3 |
| C43×3−1+2⋊C9 | 3 |
| #10624784 | 43 |