Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1062 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1062 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. C43⋊H(5,𝔽3) | C3 | semidirect |
| 2. C3×#16812526 | C3 | semidirect |
| 3. #23782892 | C3 | semidirect |
| 4. #23782891 | C3 | semidirect |
| 5. #23782890 | C3 | semidirect |
| 6. #23782889 | C3 | semidirect |
| 7. C3×#16812512 | C3 | semidirect |
| 8. #732×C43⋊C3 | C3 | semidirect |
| 9. C43×#6911 | C3 | semidirect |
| 11. C3×#11923958 | C32 | semidirect |
| 12. C3×#11923957 | C32 | semidirect |
| 13. C3×#11923956 | C32 | semidirect |
| 16. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 18. H(3,𝔽3)×C43⋊C3 | C32 | semidirect |
| 19. C32×C43⋊C9 | C32 | semidirect |
| 20. C3×C9×C43⋊C3 | C32 | semidirect |
| 21. #16812513 | C32 | semidirect |
| 22. #16812512 | C32 | semidirect |
| 23. #16812512 | C32 | semidirect |
| 24. #16812512 | C32 | semidirect |
| 25. #16812512 | C32 | semidirect |
| 26. C3×3−1+2×C43 | C32 | semidirect |
| 27. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 28. C43×#732 | C32 | semidirect |
| 74. #6911 | C43⋊C3 | semidirect |
| 87. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 93. C3×H(3,𝔽3) | C3×C43⋊C3 | semidirect |
| 101. #732 | C3×C43⋊C3 | semidirect |
| 102. C43 | #10624932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43⋊H(5,𝔽3) | 3 |
| C3×#16812526 | 3 |
| #23782892 | 3 |
| #23782891 | 3 |
| #23782890 | 3 |
| #23782889 | 3 |
| C3×#16812512 | 3 |
| #732×C43⋊C3 | 3 |
| C43×#6911 | 3 |
| #10624932 | 43 |