Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1244 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 298 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. C32×#11923958 | C3 | semidirect |
| 2. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 4. #23782805 | C3 | semidirect |
| 5. #23782804 | C3 | semidirect |
| 6. #23782801 | C3 | semidirect |
| 7. #23782798 | C3 | semidirect |
| 8. #23782795 | C3 | semidirect |
| 9. #23782783 | C3 | semidirect |
| 10. C43×#6891 | C3 | semidirect |
| 16. C3×#11923958 | C32 | semidirect |
| 17. C3×#11923957 | C32 | semidirect |
| 18. C3×#11923956 | C32 | semidirect |
| 25. C32×C43⋊C9 | C32 | semidirect |
| 26. C3×C9×C43⋊C3 | C32 | semidirect |
| 27. C32⋊(C43⋊C9) | C32 | semidirect |
| 28. C32⋊(C43⋊C9) | C32 | semidirect |
| 29. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 30. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 31. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 34. C43×C32⋊C9 | C32 | semidirect |
| 35. C43×C32⋊C9 | C32 | semidirect |
| 45. #11923958 | H(3,𝔽3) | semidirect |
| 51. C32⋊(C43⋊C3) | 3−1+2 | semidirect |
| 75. C32×C43 | C3×3−1+2 | semidirect |
| 86. C3×C43⋊C3 | C3×3−1+2 | semidirect |
| 90. C43⋊C9 | C3×H(3,𝔽3) | semidirect |
| 99. #6891 | C43⋊C3 | semidirect |
| 133. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 134. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 135. C43 | H(3,𝔽3)×3−1+2 | semidirect |
| 184. C32 | 3−1+2×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C3×3−1+2×C43⋊C3 | 3 |
| C32×C32⋊(C43⋊C3) | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782801 | 3 |
| #23782798 | 3 |
| #23782795 | 3 |
| #23782783 | 3 |
| C43×#6891 | 3 |
| H(3,𝔽3)×3−1+2 | 43 |