Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
1688 conjugacy classes of subgroups; only the 493 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 493 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 |
|---|---|---|
| 2. C32×C9×C43⋊C3 | C3 | semidirect |
| 3. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 4. C9×C32⋊(C43⋊C3) | C3 | semidirect |
| 5. #23782783 | C3 | semidirect |
| 6. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 10. H(3,𝔽3)×C43⋊C3 | C9 | direct (N × H) |
| 11. C32×C43⋊C9 | C32 | semidirect |
| 15. C3×C9×C43⋊C3 | C32 | semidirect |
| 16. C3×C9×C43⋊C3 | C32 | semidirect |
| 17. C32⋊(C43⋊C9) | C32 | semidirect |
| 18. (C3×C43⋊C3)⋊C9 | C32 | semidirect |
| 20. C32×C9×C43 | C32 | semidirect |
| 21. C43×C32⋊C9 | C32 | semidirect |
| 24. C32×C43⋊C3 | C3×C9 | semidirect |
| 27. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 34. C9×C43⋊C3 | H(3,𝔽3) | direct (N × H) |
| 36. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 43. C32×C43 | C32×C9 | semidirect |
| 49. C3×C43⋊C3 | C32×C9 | semidirect |
| 53. C9×C43 | C3×H(3,𝔽3) | semidirect |
| 55. C43⋊C9 | C3×H(3,𝔽3) | semidirect |
| 61. C9×H(3,𝔽3) | C43⋊C3 | direct (N × H) |
| 68. C43⋊C3 | C9×H(3,𝔽3) | direct (N × H) |
| 79. C32×C9 | C3×C43⋊C3 | semidirect |
| 82. C32⋊C9 | C3×C43⋊C3 | semidirect |
| 83. C43 | C3×C9×H(3,𝔽3) | semidirect |
| 91. H(3,𝔽3) | C9×C43⋊C3 | direct (N × H) |
| 111. C32 | C3×C9×C43⋊C3 | semidirect |
| 116. C9 | H(3,𝔽3)×C43⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C43⋊C3 | 3 |
| C32×C9×C43⋊C3 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782783 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C3×C9×H(3,𝔽3) | 43 |