Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 82 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. H(3,𝔽3)×C43⋊C9 | C3 | semidirect |
| 3. #23782783 | C3 | semidirect |
| 4. C3×C9×C43⋊C9 | C3 | semidirect |
| 5. #23782721 | C3 | semidirect |
| 6. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 7. #23782719 | C3 | semidirect |
| 8. #23782715 | C3 | semidirect |
| 9. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 16. #16812512 | C9 | semidirect |
| 28. C32⋊(C43⋊C3) | C3×C9 | semidirect |
| 37. C3×C43⋊C9 | C3×C9 | semidirect |
| 44. H(3,𝔽3)×C43 | C3×C9 | semidirect |
| 70. C43⋊C9 | #732 | semidirect |
| 78. H(3,𝔽3)⋊C9 | C43⋊C3 | semidirect |
| 104. C43 | C9×#732 | semidirect |
| 111. H(3,𝔽3) | C9×C43⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812512 | 3 |
| H(3,𝔽3)×C43⋊C9 | 3 |
| #23782783 | 3 |
| C3×C9×C43⋊C9 | 3 |
| #23782721 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| #23782715 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| C9×#732 | 43 |