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. #31771155 | C2 | semidirect |
| 2. #31770902 | C2 | semidirect |
| 3. #31770890 | C2 | semidirect |
| 4. #31770885 | C2 | semidirect |
| 5. #31770856 | C2 | semidirect |
| 6. #31770853 | C2 | semidirect |
| 7. #31770817 | C2 | semidirect |
| 8. #31770805 | C2 | semidirect |
| 9. #31770800 | C2 | semidirect |
| 10. #31770629 | C2 | semidirect |
| 11. #529×C269 | C2 | semidirect |
| 141. C269 | #3251 | semidirect |
| 144. #529 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771155 | 2 |
| #31770902 | 2 |
| #31770890 | 2 |
| #31770885 | 2 |
| #31770856 | 2 |
| #31770853 | 2 |
| #31770817 | 2 |
| #31770805 | 2 |
| #31770800 | 2 |
| #31770629 | 2 |
| #529×C269 | 2 |
| #3251 | 269 |