Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31771160 | C2 | semidirect |
| 3. #31770892 | C2 | semidirect |
| 4. #31770889 | C2 | semidirect |
| 5. #31770835 | C2 | semidirect |
| 6. #31770833 | C2 | semidirect |
| 7. #31770811 | C2 | semidirect |
| 8. #31770810 | C2 | semidirect |
| 9. #31770804 | C2 | semidirect |
| 10. C4⋊C8×D269 | C2 | semidirect |
| 11. #476×C269 | C2 | semidirect |
| 102. C4×D269 | SD16 | semidirect |
| 142. C269 | #3246 | semidirect |
| 147. #476 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| #31771152 | 2 |
| #31770892 | 2 |
| #31770889 | 2 |
| #31770835 | 2 |
| #31770833 | 2 |
| #31770811 | 2 |
| #31770810 | 2 |
| #31770804 | 2 |
| C4⋊C8×D269 | 2 |
| #476×C269 | 2 |
| #3246 | 269 |