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. #31771137 | C2 | semidirect |
| 3. #31770904 | C2 | semidirect |
| 4. #31770897 | C2 | semidirect |
| 5. #31770840 | C2 | semidirect |
| 6. #31770835 | C2 | semidirect |
| 7. #31770819 | C2 | semidirect |
| 8. #31770806 | C2 | semidirect |
| 9. #31770800 | C2 | semidirect |
| 10. C4⋊C8×D269 | C2 | semidirect |
| 11. #476×C269 | C2 | semidirect |
| 141. C269 | #3247 | semidirect |
| 147. #476 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| #31771137 | 2 |
| #31770904 | 2 |
| #31770897 | 2 |
| #31770840 | 2 |
| #31770835 | 2 |
| #31770819 | 2 |
| #31770806 | 2 |
| #31770800 | 2 |
| C4⋊C8×D269 | 2 |
| #476×C269 | 2 |
| #3247 | 269 |