Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
948 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 268 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. #23782924 | C3 | semidirect |
| 2. C3×#16812526 | C3 | semidirect |
| 3. #23782902 | C3 | semidirect |
| 4. #23782901 | C3 | semidirect |
| 5. #23782896 | C3 | semidirect |
| 6. #23782881 | C3 | semidirect |
| 7. #23782875 | C3 | semidirect |
| 8. C3×#16812509 | C3 | semidirect |
| 9. C43×#6911 | C3 | semidirect |
| 12. #16812524 | C32 | semidirect |
| 16. C3×#11923957 | C32 | semidirect |
| 17. C3×#11923956 | C32 | semidirect |
| 20. C3×C9×C43⋊C3 | C32 | semidirect |
| 21. #16812515 | C32 | semidirect |
| 22. #16812509 | C32 | semidirect |
| 23. #16812509 | C32 | semidirect |
| 24. #16812509 | C32 | semidirect |
| 25. #16812506 | C32 | semidirect |
| 71. #6911 | C43⋊C3 | semidirect |
| 99. C43 | #10624935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782924 | 3 |
| C3×#16812526 | 3 |
| #23782902 | 3 |
| #23782901 | 3 |
| #23782896 | 3 |
| #23782881 | 3 |
| #23782875 | 3 |
| C3×#16812509 | 3 |
| C43×#6911 | 3 |
| #10624935 | 43 |