Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782819 | C3 | semidirect |
| 3. #23782779 | C3 | semidirect |
| 4. C3×(C43⋊C9)⋊C9 | C3 | semidirect |
| 5. #23782725 | C3 | semidirect |
| 6. #23782725 | C3 | semidirect |
| 7. #23782724 | C3 | semidirect |
| 8. #23782724 | C3 | semidirect |
| 9. #23782722 | C3 | semidirect |
| 10. #23782722 | C3 | semidirect |
| 126. C43 | #10624827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782819 | 3 |
| #23782806 | 3 |
| #23782779 | 3 |
| C3×(C43⋊C9)⋊C9 | 3 |
| #23782725 | 3 |
| #23782724 | 3 |
| #23782722 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| #10624827 | 43 |