Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771142 | C2 | semidirect |
| 3. #31770908 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770842 | C2 | semidirect |
| 6. #31770837 | C2 | semidirect |
| 7. #31770823 | C2 | semidirect |
| 8. #31770805 | C2 | semidirect |
| 9. #31770801 | C2 | semidirect |
| 10. C4⋊C8×D269 | C2 | semidirect |
| 11. #477×C269 | C2 | semidirect |
| 141. C269 | #3247 | semidirect |
| 146. #477 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| #31771142 | 2 |
| #31770908 | 2 |
| #31770892 | 2 |
| #31770842 | 2 |
| #31770837 | 2 |
| #31770823 | 2 |
| #31770805 | 2 |
| #31770801 | 2 |
| C4⋊C8×D269 | 2 |
| #477×C269 | 2 |
| #3247 | 269 |