Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
936 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|---|
| 3. #23782896 | C3 | semidirect |
| 4. #23782895 | C3 | semidirect |
| 5. #23782894 | C3 | semidirect |
| 6. #23782893 | C3 | semidirect |
| 7. C3×#16812514 | C3 | semidirect |
| 8. #733×C43⋊C3 | C3 | semidirect |
| 9. C43×#6912 | C3 | semidirect |
| 72. #6912 | C43⋊C3 | semidirect |
| 98. C43 | #10624933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782923 | 3 |
| C3×#16812526 | 3 |
| #23782896 | 3 |
| #23782895 | 3 |
| #23782894 | 3 |
| #23782893 | 3 |
| C3×#16812514 | 3 |
| #733×C43⋊C3 | 3 |
| C43×#6912 | 3 |
| #10624933 | 43 |