Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
432 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 67 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×C9×C43⋊C3 | C3 | semidirect |
| 3. #23782816 | C3 | semidirect |
| 4. #23782815 | C3 | semidirect |
| 5. #23782722 | C3 | semidirect |
| 6. #23782722 | C3 | semidirect |
| 7. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 8. #23782711 | C3 | semidirect |
| 9. C43×C9⋊H(3,𝔽3) | C3 | semidirect |
| 33. C32×C43⋊C3 | 3−1+2 | semidirect |
| 71. C9×C43 | AΣL(1,𝔽27) | semidirect |
| 81. C9⋊H(3,𝔽3) | C43⋊C3 | semidirect |
| 112. C43 | #10624784 | semidirect |
| 159. C9 | #16812506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C43⋊C3 | 3 |
| C3×#16812506 | 3 |
| #23782816 | 3 |
| #23782815 | 3 |
| #23782722 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782711 | 3 |
| C43×C9⋊H(3,𝔽3) | 3 |
| #10624784 | 43 |