Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
980 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 980 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. #23782923 | C3 | semidirect |
| 2. #23782905 | C3 | semidirect |
| 3. #23782896 | C3 | semidirect |
| 4. #23782892 | C3 | semidirect |
| 5. #23782887 | C3 | semidirect |
| 6. #23782877 | C3 | semidirect |
| 7. C3×#16812507 | C3 | semidirect |
| 8. C32×3−1+2×C43 | C3 | semidirect |
| 10. #16812525 | C32 | semidirect |
| 14. #16812515 | C32 | semidirect |
| 15. #16812513 | C32 | semidirect |
| 16. #16812510 | C32 | semidirect |
| 17. #16812507 | C32 | semidirect |
| 18. #16812507 | C32 | semidirect |
| 24. C3×3−1+2×C43 | C32 | semidirect |
| 25. C32×C9×C43 | C32 | semidirect |
| 65. C32×3−1+2 | C43⋊C3 | semidirect |
| 87. C3×3−1+2 | C3×C43⋊C3 | semidirect |
| 89. C32×C9 | C3×C43⋊C3 | semidirect |
| 95. C43 | #10624934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782923 | 3 |
| #23782905 | 3 |
| #23782896 | 3 |
| #23782892 | 3 |
| #23782887 | 3 |
| #23782877 | 3 |
| C3×#16812507 | 3 |
| C32×3−1+2×C43 | 3 |
| #10624934 | 43 |