Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
718 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 298 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. #23782847 | C3 | semidirect |
| 3. #23782844 | C3 | semidirect |
| 4. #23782828 | C3 | semidirect |
| 5. #23782825 | C3 | semidirect |
| 6. #23782819 | C3 | semidirect |
| 7. #23782817 | C3 | semidirect |
| 8. #23782816 | C3 | semidirect |
| 9. #23782810 | C3 | semidirect |
| 12. 3−1+2×C43⋊C9 | C3 | semidirect |
| 13. C9×#11923956 | C3 | semidirect |
| 14. C3×#16812500 | C3 | semidirect |
| 15. C9×3−1+2×C43 | C3 | semidirect |
| 73. 3−1+2×C43 | 3−1+2 | semidirect |
| 90. C9×C43 | #737 | semidirect |
| 113. C9×3−1+2 | C43⋊C3 | semidirect |
| 157. C43 | #10624901 | semidirect |
| 165. 3−1+2 | #11923956 | 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 |
| #23782847 | 3 |
| #23782844 | 3 |
| #23782828 | 3 |
| #23782825 | 3 |
| #23782819 | 3 |
| #23782817 | 3 |
| #23782816 | 3 |
| #23782810 | 3 |
| #23782804 | 3 |
| #23782803 | 3 |
| 3−1+2×C43⋊C9 | 3 |
| C9×#11923956 | 3 |
| C3×#16812500 | 3 |
| C9×3−1+2×C43 | 3 |
| #10624901 | 43 |