Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
304 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C9×#11923958 | C3 | semidirect |
| 3. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 4. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. #23782725 | C3 | semidirect |
| 7. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 8. 3−1+2⋊(C43⋊C9) | C3 | semidirect |
| 9. #23782719 | C3 | semidirect |
| 10. #23782719 | C3 | semidirect |
| 11. #23782711 | C3 | semidirect |
| 12. #23782711 | C3 | semidirect |
| 13. C9×3−1+2×C43 | C3 | semidirect |
| 20. #16812508 | C9 | semidirect |
| 46. C32×C43⋊C3 | C3×C9 | semidirect |
| 48. #11923958 | C3×C9 | semidirect |
| 63. 3−1+2×C43 | C3×C9 | semidirect |
| 103. C9×3−1+2 | C43⋊C3 | semidirect |
| 148. C43 | AΣL(1,𝔽27)⋊C9 | semidirect |
| 160. 3−1+2 | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812508 | 3 |
| C9×#11923958 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| #23782725 | 3 |
| 3−1+2⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| #23782711 | 3 |
| C9×3−1+2×C43 | 3 |
| AΣL(1,𝔽27)⋊C9 | 43 |