Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4×Q8×D269 | C2 | semidirect |
| 3. #31770920 | C2 | semidirect |
| 4. #31770897 | C2 | semidirect |
| 5. #31770806 | C2 | semidirect |
| 6. #31770805 | C2 | semidirect |
| 7. #31770745 | C2 | semidirect |
| 8. #31770708 | C2 | semidirect |
| 9. #31770704 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #477×C269 | C2 | semidirect |
| 87. Dic538 | #41 | semidirect |
| 108. Q8×C269 | #41 | semidirect |
| 140. C269 | #3112 | semidirect |
| 146. #477 | D269 | semidirect |
| 231. Q8 | #16864403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| C4×Q8×D269 | 2 |
| #31770920 | 2 |
| #31770897 | 2 |
| #31770806 | 2 |
| #31770805 | 2 |
| #31770745 | 2 |
| #31770708 | 2 |
| #31770704 | 2 |
| #31770661 | 2 |
| #477×C269 | 2 |
| #3112 | 269 |