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. #31771260 | C2 | semidirect |
| 2. #31770957 | C2 | semidirect |
| 3. #31770946 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770832 | C2 | semidirect |
| 6. #31770810 | C2 | semidirect |
| 7. #31770748 | C2 | semidirect |
| 8. C4×#16864387 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. #31770599 | C2 | semidirect |
| 11. #555×C269 | C2 | semidirect |
| 130. C269 | #3303 | semidirect |
| 132. #555 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771260 | 2 |
| #31770957 | 2 |
| #31770946 | 2 |
| #31770892 | 2 |
| #31770832 | 2 |
| #31770810 | 2 |
| #31770748 | 2 |
| C4×#16864387 | 2 |
| D4×#14524130 | 2 |
| #31770599 | 2 |
| #555×C269 | 2 |
| #3303 | 269 |