Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1232 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 1232 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. C3×3−1+2×C43⋊C3 | C3 | semidirect |
| 3. C32×C9×C43⋊C3 | C3 | semidirect |
| 4. #23782809 | C3 | semidirect |
| 5. #23782808 | C3 | semidirect |
| 6. #23782807 | C3 | semidirect |
| 7. #23782806 | C3 | semidirect |
| 8. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 9. C43×#6893 | C3 | semidirect |
| 12. C3×#11923958 | C32 | semidirect |
| 13. C3×#11923957 | C32 | semidirect |
| 14. C3×#11923956 | C32 | semidirect |
| 19. C32×C43⋊C9 | C32 | semidirect |
| 23. C3×C9×C43⋊C3 | C32 | semidirect |
| 24. C32⋊(C43⋊C9) | C32 | semidirect |
| 25. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 26. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 27. C3×3−1+2×C43 | C32 | semidirect |
| 29. C32×C9×C43 | C32 | semidirect |
| 30. C43×C32⋊C9 | C32 | semidirect |
| 81. #6893 | C43⋊C3 | direct (N × H) |
| 89. C43⋊C3 | #6893 | direct (N × H) |
| 96. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 106. C32×C9 | C3×C43⋊C3 | semidirect |
| 110. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 111. C43 | C3×#6893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C43⋊C3 | 3 |
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| #23782809 | 3 |
| #23782808 | 3 |
| #23782807 | 3 |
| #23782806 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C43×#6893 | 3 |
| C3×#6893 | 43 |