Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
414 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 70 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. #23782896 | C3 | semidirect |
| 2. #23782895 | C3 | semidirect |
| 3. #23782895 | C3 | semidirect |
| 4. #23782888 | C3 | semidirect |
| 5. #23782887 | C3 | semidirect |
| 6. #23782883 | C3 | semidirect |
| 7. #23782882 | C3 | semidirect |
| 8. #23782882 | C3 | semidirect |
| 9. C3×#16812514 | C3 | semidirect |
| 10. C3×#16812511 | C3 | semidirect |
| 11. #23782809 | C3 | semidirect |
| 12. #23782806 | C3 | semidirect |
| 13. C43×3−1+4 | C3 | semidirect |
| 120. 3−1+4 | C43⋊C3 | semidirect |
| 170. C43 | #10624750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782896 | 3 |
| #23782895 | 3 |
| #23782888 | 3 |
| #23782887 | 3 |
| #23782883 | 3 |
| #23782882 | 3 |
| C3×#16812514 | 3 |
| C3×#16812511 | 3 |
| #23782809 | 3 |
| #23782806 | 3 |
| C43×3−1+4 | 3 |
| #10624750 | 43 |