Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic269 | C2 | semidirect |
| 3. #31770919 | C2 | semidirect |
| 4. #31770916 | C2 | semidirect |
| 5. #31770898 | C2 | semidirect |
| 6. #31770803 | C2 | semidirect |
| 7. #31770744 | C2 | semidirect |
| 8. #31770708 | C2 | semidirect |
| 9. #31770706 | C2 | semidirect |
| 10. #31770659 | C2 | semidirect |
| 11. #448×C269 | C2 | semidirect |
| 104. Q8×C269 | #41 | semidirect |
| 140. C269 | #3112 | semidirect |
| 149. #448 | D269 | semidirect |
| 229. Q8 | #16864401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771150 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770919 | 2 |
| #31770916 | 2 |
| #31770898 | 2 |
| #31770803 | 2 |
| #31770744 | 2 |
| #31770708 | 2 |
| #31770706 | 2 |
| #31770659 | 2 |
| #448×C269 | 2 |
| #3112 | 269 |