Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C4⋊Q8×D269 | C2 | semidirect |
| 4. #31770816 | C2 | semidirect |
| 5. #31770814 | C2 | semidirect |
| 6. #31770812 | C2 | semidirect |
| 7. #31770810 | C2 | semidirect |
| 8. #31770808 | C2 | semidirect |
| 9. #31770627 | C2 | semidirect |
| 10. #31770612 | C2 | semidirect |
| 11. #461×C269 | C2 | semidirect |
| 131. C4×C269 | #137 | semidirect |
| 139. Dic269 | #137 | semidirect |
| 145. C269 | #3039 | semidirect |
| 155. #461 | D269 | semidirect |
| 283. C4 | #22575482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575482 | 2 |
| C4⋊Q8×D269 | 2 |
| C4×#16864401 | 2 |
| #31770816 | 2 |
| #31770814 | 2 |
| #31770812 | 2 |
| #31770810 | 2 |
| #31770808 | 2 |
| #31770627 | 2 |
| #31770612 | 2 |
| #461×C269 | 2 |
| #3039 | 269 |