Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
992 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 292 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. C3×#16812525 | C3 | semidirect |
| 2. C32×#11923956 | C3 | semidirect |
| 3. #23782900 | C3 | direct (N × H) |
| 4. C3×#16812514 | C3 | semidirect |
| 5. C3×#16812512 | C3 | semidirect |
| 6. C3×#16812511 | C3 | semidirect |
| 7. C3×#16812509 | C3 | semidirect |
| 8. C3×#16812508 | C3 | semidirect |
| 9. C3×#16812506 | C3 | semidirect |
| 10. C3×C43×#737 | C3 | semidirect |
| 13. #16812525 | C32 | semidirect |
| 21. C3×#11923956 | C32 | semidirect |
| 26. #16812514 | C32 | semidirect |
| 27. #16812512 | C32 | semidirect |
| 28. #16812511 | C32 | semidirect |
| 29. #16812509 | C32 | semidirect |
| 30. #16812508 | C32 | semidirect |
| 31. #16812506 | C32 | semidirect |
| 33. C43×#737 | C32 | semidirect |
| 97. C3×#737 | C43⋊C3 | semidirect |
| 109. C3×C43 | #6913 | semidirect |
| 117. #737 | C3×C43⋊C3 | semidirect |
| 141. C43 | C3×#6913 | semidirect |
| 203. C3 | #23782900 | 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 |
| C32×#11923956 | 3 |
| #23782900 | 3 |
| C3×#16812514 | 3 |
| C3×#16812512 | 3 |
| C3×#16812511 | 3 |
| C3×#16812509 | 3 |
| C3×#16812508 | 3 |
| C3×#16812506 | 3 |
| C3×C43×#737 | 3 |
| C3×#6913 | 43 |