Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
848 conjugacy classes of subgroups; only the 454 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 454 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 | direct (N × H) |
| 3. C3×#16812505 | C3 | semidirect |
| 4. C3×#16812504 | C3 | semidirect |
| 5. C3×#16812503 | C3 | semidirect |
| 6. C32×C43⋊C27 | C3 | semidirect |
| 7. C3×C27×C43⋊C3 | C3 | semidirect |
| 8. C3×C43×C27⋊C3 | C3 | semidirect |
| 16. #16812505 | C32 | semidirect |
| 17. #16812504 | C32 | semidirect |
| 18. #16812503 | C32 | semidirect |
| 23. C3×C43⋊C27 | C32 | semidirect |
| 24. C27×C43⋊C3 | C32 | semidirect |
| 26. C43×C27⋊C3 | C32 | semidirect |
| 63. C3×C27⋊C3 | C43⋊C3 | semidirect |
| 67. C3×C43 | #6903 | semidirect |
| 81. C27⋊C3 | C3×C43⋊C3 | semidirect |
| 89. C43 | C3×#6903 | semidirect |
| 121. C3 | #23782858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782858 | 3 |
| C3×#16812505 | 3 |
| C3×#16812504 | 3 |
| C3×#16812503 | 3 |
| C32×C43⋊C27 | 3 |
| C3×C27×C43⋊C3 | 3 |
| C3×C43×C27⋊C3 | 3 |
| C3×#6903 | 43 |