Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 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 |
|---|---|---|
| 2. #23782849 | C3 | semidirect |
| 3. #23782841 | C3 | semidirect |
| 4. #23782828 | C3 | semidirect |
| 5. #23782826 | C3 | semidirect |
| 6. #23782817 | C3 | semidirect |
| 7. #23782816 | C3 | semidirect |
| 8. #23782812 | C3 | semidirect |
| 11. #11923957⋊C9 | C3 | semidirect |
| 12. #11923957⋊C9 | C3 | semidirect |
| 13. #23782779 | C3 | semidirect |
| 14. C3×C9×C43⋊C9 | C3 | semidirect |
| 15. C43×#6894 | C3 | semidirect |
| 61. C3×C43⋊C9 | 3−1+2 | semidirect |
| 90. C9×C43 | #737 | semidirect |
| 99. C43⋊C9 | #737 | semidirect |
| 108. #6894 | C43⋊C3 | semidirect |
| 157. C43 | #10624879 | 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 |
| #23782849 | 3 |
| #23782841 | 3 |
| #23782828 | 3 |
| #23782826 | 3 |
| #23782817 | 3 |
| #23782816 | 3 |
| #23782812 | 3 |
| #23782805 | 3 |
| #23782802 | 3 |
| #11923957⋊C9 | 3 |
| #23782779 | 3 |
| C3×C9×C43⋊C9 | 3 |
| C43×#6894 | 3 |
| #10624879 | 43 |