Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
978 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
| 3. C3×#16812525 | C3 | semidirect |
| 4. #23782888 | C3 | semidirect |
| 5. #23782886 | C3 | semidirect |
| 6. #23782885 | C3 | semidirect |
| 7. #23782884 | C3 | semidirect |
| 8. C3×#16812510 | C3 | semidirect |
| 9. #731×C43⋊C3 | C3 | semidirect |
| 10. C3×C43×#731 | C3 | semidirect |
| 15. C3×#11923958 | C32 | semidirect |
| 16. C3×#11923958 | C32 | semidirect |
| 17. C3×#11923957 | C32 | semidirect |
| 18. C3×#11923956 | C32 | semidirect |
| 19. 3−1+2×C43⋊C3 | C32 | semidirect |
| 25. C3×C9×C43⋊C3 | C32 | semidirect |
| 26. #16812511 | C32 | semidirect |
| 27. #16812510 | C32 | semidirect |
| 28. #16812510 | C32 | semidirect |
| 29. #16812510 | C32 | semidirect |
| 30. #16812509 | C32 | semidirect |
| 31. C3×3−1+2×C43 | C32 | semidirect |
| 33. C32×C9×C43 | C32 | semidirect |
| 34. C43×#731 | C32 | semidirect |
| 35. C43×#731 | C32 | semidirect |
| 36. C43×#731 | C32 | semidirect |
| 98. C3×#731 | C43⋊C3 | semidirect |
| 115. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 123. C32×C9 | C3×C43⋊C3 | semidirect |
| 129. #731 | C3×C43⋊C3 | semidirect |
| 130. #731 | C3×C43⋊C3 | semidirect |
| 131. #731 | C3×C43⋊C3 | semidirect |
| 132. C43 | #10624931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782923 | 3 |
| C43⋊H(5,𝔽3) | 3 |
| C3×#16812525 | 3 |
| #23782888 | 3 |
| #23782886 | 3 |
| #23782885 | 3 |
| #23782884 | 3 |
| C3×#16812510 | 3 |
| #731×C43⋊C3 | 3 |
| C3×C43×#731 | 3 |
| #10624931 | 43 |