Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 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. #23782796 | C3 | semidirect |
| 3. C3×(C3×C43⋊C3)⋊C9 | C3 | semidirect |
| 4. C32⋊C9×C43⋊C3 | C3 | semidirect |
| 5. #23782721 | C3 | semidirect |
| 6. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 7. #23782719 | C3 | semidirect |
| 8. #23782719 | C3 | semidirect |
| 9. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 102. H(3,𝔽3)⋊C9 | C43⋊C3 | semidirect |
| 135. C43 | #10624820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782796 | 3 |
| (C3×C43⋊C3)⋊H(3,𝔽3) | 3 |
| C3×(C3×C43⋊C3)⋊C9 | 3 |
| C32⋊C9×C43⋊C3 | 3 |
| #23782721 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| #10624820 | 43 |