Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
190 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 46 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. #23782905 | C3 | semidirect |
| 2. #23782892 | C3 | semidirect |
| 3. #23782767 | C3 | semidirect |
| 4. #23782757 | C3 | semidirect |
| 5. #23782757 | C3 | semidirect |
| 6. #23782751 | C3 | semidirect |
| 7. #23782747 | C3 | semidirect |
| 8. #23782746 | C3 | semidirect |
| 9. C43×#6899 | C3 | semidirect |
| 12. #16812515 | C32 | semidirect |
| 13. #16812515 | C32 | semidirect |
| 18. #16812513 | C32 | semidirect |
| 23. C43×C9⋊C9 | C32 | semidirect |
| 25. C92×C43 | C32 | semidirect |
| 60. #6899 | C43⋊C3 | semidirect |
| 87. C9⋊C9 | C3×C43⋊C3 | semidirect |
| 89. C92 | C3×C43⋊C3 | semidirect |
| 90. C43 | #10624853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782905 | 3 |
| #23782892 | 3 |
| #23782767 | 3 |
| #23782757 | 3 |
| #23782751 | 3 |
| #23782747 | 3 |
| #23782746 | 3 |
| C43×#6899 | 3 |
| #10624853 | 43 |