Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
828 conjugacy classes of subgroups; only the 448 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 448 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. #23782858 | C3 | semidirect |
| 3. #23782856 | C3 | semidirect |
| 4. C3×#16812505 | C3 | semidirect |
| 5. C27⋊C3×C43⋊C3 | C3 | semidirect |
| 6. C3×C43×C27⋊C3 | C3 | semidirect |
| 18. #16812505 | C32 | semidirect |
| 19. #16812505 | C32 | semidirect |
| 20. #16812504 | C32 | semidirect |
| 21. #16812503 | C32 | semidirect |
| 22. C3×C43⋊C27 | C32 | semidirect |
| 23. C27×C43⋊C3 | C32 | semidirect |
| 26. C43×C27⋊C3 | C32 | semidirect |
| 27. C3×C27×C43 | C32 | semidirect |
| 70. C3×C27⋊C3 | C43⋊C3 | semidirect |
| 93. C27⋊C3 | C3×C43⋊C3 | semidirect |
| 96. C3×C27 | C3×C43⋊C3 | semidirect |
| 97. C43 | #10624918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782858 | 3 |
| #23782856 | 3 |
| C3×#16812505 | 3 |
| C27⋊C3×C43⋊C3 | 3 |
| C3×C43×C27⋊C3 | 3 |
| #10624918 | 43 |