Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #31771320 | C2 | semidirect |
| 2. #31771260 | C2 | semidirect |
| 3. #31770956 | C2 | semidirect |
| 4. #31770947 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770834 | C2 | semidirect |
| 7. #31770811 | C2 | semidirect |
| 8. #31770752 | C2 | semidirect |
| 9. C4×D2152 | C2 | semidirect |
| 10. #31770602 | C2 | semidirect |
| 11. C8×D4×C269 | C2 | semidirect |
| 130. C269 | #3303 | semidirect |
| 141. C8×D4 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31771260 | 2 |
| #31770956 | 2 |
| #31770947 | 2 |
| #31770896 | 2 |
| #31770834 | 2 |
| #31770811 | 2 |
| #31770752 | 2 |
| C4×D2152 | 2 |
| #31770602 | 2 |
| C8×D4×C269 | 2 |
| #3303 | 269 |