Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
456 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 70 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. #23782886 | C3 | semidirect |
| 2. #23782882 | C3 | semidirect |
| 3. #23782881 | C3 | semidirect |
| 4. C3×#16812512 | C3 | semidirect |
| 5. C3×#16812509 | C3 | semidirect |
| 6. #23782806 | C3 | semidirect |
| 7. C43×H(5,𝔽3) | C3 | semidirect |
| 8. C3×#11923958 | C32 | semidirect |
| 9. C3×#11923958 | C32 | semidirect |
| 10. C3×C32⋊(C43⋊C3) | C32 | semidirect |
| 11. C32×C43⋊C9 | C32 | semidirect |
| 67. H(5,𝔽3) | C43⋊C3 | semidirect |
| 98. C43 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782886 | 3 |
| #23782882 | 3 |
| #23782881 | 3 |
| C3×#16812512 | 3 |
| C3×#16812509 | 3 |
| #23782806 | 3 |
| C43×H(5,𝔽3) | 3 |
| #10624748 | 43 |