Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31771156 | C2 | semidirect |
| 2. C4×#16864401 | C2 | semidirect |
| 3. #31770932 | C2 | semidirect |
| 4. #31770887 | C2 | semidirect |
| 5. #31770806 | C2 | semidirect |
| 6. #31770800 | C2 | semidirect |
| 7. #31770751 | C2 | semidirect |
| 8. #31770714 | C2 | semidirect |
| 9. #31770704 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 86. Dic538 | #41 | semidirect |
| 109. D4×C269 | #41 | semidirect |
| 144. C269 | #3115 | semidirect |
| 150. #474 | D269 | semidirect |
| 241. D4 | #16864403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| C4×#16864401 | 2 |
| #31770932 | 2 |
| #31770887 | 2 |
| #31770806 | 2 |
| #31770800 | 2 |
| #31770751 | 2 |
| #31770714 | 2 |
| #31770704 | 2 |
| #31770661 | 2 |
| #474×C269 | 2 |
| #3115 | 269 |