Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
948 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 286 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. #23782923 | C3 | semidirect |
| 2. C3×#16812526 | C3 | semidirect |
| 3. #23782900 | C3 | semidirect |
| 4. #23782899 | C3 | semidirect |
| 5. #23782895 | C3 | semidirect |
| 6. #23782891 | C3 | semidirect |
| 7. #23782883 | C3 | semidirect |
| 8. #23782881 | C3 | semidirect |
| 9. #23782874 | C3 | semidirect |
| 10. C3×#16812511 | C3 | semidirect |
| 11. C3×#16812509 | C3 | semidirect |
| 12. C43×3−1+4 | C3 | semidirect |
| 17. #16812525 | C32 | semidirect |
| 21. C3×#11923957 | C32 | semidirect |
| 22. C3×#11923956 | C32 | semidirect |
| 27. C3×C9×C43⋊C3 | C32 | semidirect |
| 28. #16812514 | C32 | semidirect |
| 30. #16812511 | C32 | semidirect |
| 31. #16812511 | C32 | semidirect |
| 32. #16812511 | C32 | semidirect |
| 33. #16812509 | C32 | semidirect |
| 34. #16812509 | C32 | semidirect |
| 35. #16812509 | C32 | semidirect |
| 36. #16812508 | C32 | semidirect |
| 37. #16812506 | C32 | semidirect |
| 39. C43×#737 | C32 | semidirect |
| 106. 3−1+4 | C43⋊C3 | semidirect |
| 130. #737 | C3×C43⋊C3 | semidirect |
| 155. C43 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782923 | 3 |
| C3×#16812526 | 3 |
| #23782900 | 3 |
| #23782899 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782883 | 3 |
| #23782881 | 3 |
| #23782874 | 3 |
| C3×#16812511 | 3 |
| C3×#16812509 | 3 |
| C43×3−1+4 | 3 |
| #10624935 | 43 |