Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
470 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 470 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. C3×#16812524 | C3 | semidirect |
| 2. C3×#16812514 | C3 | semidirect |
| 3. C3×#16812512 | C3 | semidirect |
| 4. C3×#16812511 | C3 | semidirect |
| 5. C3×#16812509 | C3 | semidirect |
| 6. C3×#16812507 | C3 | semidirect |
| 7. #23782809 | C3 | semidirect |
| 8. C3×C32⋊(C43⋊C9) | C3 | semidirect |
| 9. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 105. C3×AΣL(1,𝔽27) | C43⋊C3 | semidirect |
| 140. C43 | #10624746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812524 | 3 |
| C3×#16812514 | 3 |
| C3×#16812512 | 3 |
| C3×#16812511 | 3 |
| C3×#16812509 | 3 |
| C3×#16812507 | 3 |
| #23782809 | 3 |
| C3×C32⋊(C43⋊C9) | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624746 | 43 |