Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
730 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 280 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. #23782821 | C3 | semidirect |
| 3. #23782819 | C3 | semidirect |
| 4. #23782818 | C3 | semidirect |
| 5. #23782815 | C3 | semidirect |
| 6. #23782814 | C3 | semidirect |
| 7. #23782812 | C3 | semidirect |
| 8. #23782811 | C3 | semidirect |
| 9. #23782810 | C3 | semidirect |
| 10. #23782810 | C3 | semidirect |
| 13. C3×#16812500 | C3 | semidirect |
| 14. C9⋊C9×C43⋊C3 | C3 | semidirect |
| 15. C43×#6894 | C3 | semidirect |
| 90. C9×C43 | #737 | semidirect |
| 110. #6894 | C43⋊C3 | semidirect |
| 157. C43 | #10624900 | semidirect |
| 203. C9 | #16812526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812526 | 3 |
| #23782821 | 3 |
| #23782819 | 3 |
| #23782818 | 3 |
| #23782815 | 3 |
| #23782814 | 3 |
| #23782812 | 3 |
| #23782811 | 3 |
| #23782810 | 3 |
| C9×C32⋊(C43⋊C3) | 3 |
| #23782783 | 3 |
| C3×#16812500 | 3 |
| C9⋊C9×C43⋊C3 | 3 |
| C43×#6894 | 3 |
| #10624900 | 43 |