Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
280 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #23782805 | C3 | semidirect |
| 3. #23782804 | C3 | semidirect |
| 4. #23782800 | C3 | semidirect |
| 5. C3×C9×C43⋊C9 | C3 | semidirect |
| 6. #23782721 | C3 | semidirect |
| 7. #23782721 | C3 | semidirect |
| 8. H(3,𝔽3)⋊(C43⋊C9) | C3 | semidirect |
| 9. #23782719 | C3 | semidirect |
| 10. #23782719 | C3 | semidirect |
| 11. #23782715 | C3 | semidirect |
| 12. #23782715 | C3 | semidirect |
| 13. C43×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 59. C3×C43⋊C9 | 3−1+2 | semidirect |
| 99. C43⋊C9 | #732 | semidirect |
| 110. H(3,𝔽3)⋊C9 | C43⋊C3 | semidirect |
| 145. C43 | #10624786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812512 | 3 |
| #23782805 | 3 |
| #23782804 | 3 |
| #23782800 | 3 |
| C3×C9×C43⋊C9 | 3 |
| #23782721 | 3 |
| H(3,𝔽3)⋊(C43⋊C9) | 3 |
| #23782719 | 3 |
| #23782715 | 3 |
| C43×H(3,𝔽3)⋊C9 | 3 |
| #10624786 | 43 |