Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
212 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #23782739 | C3 | semidirect |
| 5. #23782738 | C3 | semidirect |
| 6. #23782737 | C3 | semidirect |
| 7. #23782736 | C3 | semidirect |
| 8. #23782735 | C3 | semidirect |
| 9. C43×#6875 | C3 | semidirect |
| 16. #16812504 | C9 | semidirect |
| 18. #16812503 | C9 | semidirect |
| 20. C27×C43⋊C3 | C9 | semidirect |
| 40. C43⋊C27 | C3×C9 | semidirect |
| 44. C27×C43 | C3×C9 | semidirect |
| 67. #6875 | C43⋊C3 | direct (N × H) |
| 72. C43⋊C3 | #6875 | direct (N × H) |
| 90. C43 | C3×#6875 | semidirect |
| 108. C27 | C9×C43⋊C3 | 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 |
| C9⋊C9×C43⋊C3 | 3 |
| #23782739 | 3 |
| #23782738 | 3 |
| #23782737 | 3 |
| #23782736 | 3 |
| #23782735 | 3 |
| C43×#6875 | 3 |
| C3×#6875 | 43 |