Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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×#16812525 | C3 | semidirect |
| 2. #23782905 | C3 | semidirect |
| 3. #23782896 | C3 | semidirect |
| 4. #23782892 | C3 | semidirect |
| 5. #23782887 | C3 | semidirect |
| 6. #23782882 | C3 | semidirect |
| 7. #23782877 | C3 | semidirect |
| 8. C3×C43×#737 | C3 | semidirect |
| 12. #16812525 | C32 | semidirect |
| 13. #16812525 | C32 | semidirect |
| 19. #16812515 | C32 | semidirect |
| 21. #16812510 | C32 | semidirect |
| 22. #16812507 | C32 | semidirect |
| 28. C3×3−1+2×C43 | C32 | semidirect |
| 31. C32×C9×C43 | C32 | semidirect |
| 76. C3×#737 | C43⋊C3 | semidirect |
| 101. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 106. C32×C9 | C3×C43⋊C3 | semidirect |
| 111. C43 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782905 | 3 |
| #23782896 | 3 |
| #23782892 | 3 |
| #23782887 | 3 |
| #23782882 | 3 |
| #23782877 | 3 |
| C3×C43×#737 | 3 |
| #10624929 | 43 |