Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31770957 | C2 | semidirect |
| 4. #31770942 | C2 | semidirect |
| 5. #31770847 | C2 | semidirect |
| 6. #31770816 | C2 | semidirect |
| 7. #31770762 | C2 | semidirect |
| 8. C4×#16864392 | C2 | semidirect |
| 10. #103×D269 | C2 | semidirect |
| 11. #477×C269 | C2 | semidirect |
| 82. D1076 | Q16 | semidirect |
| 122. C269 | #3299 | semidirect |
| 128. #477 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771316 | 2 |
| Q8×D1076 | 2 |
| #31770957 | 2 |
| #31770942 | 2 |
| #31770847 | 2 |
| #31770816 | 2 |
| #31770762 | 2 |
| C4×#16864392 | 2 |
| #31770670 | 2 |
| #103×D269 | 2 |
| #477×C269 | 2 |
| #3299 | 269 |