Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771276 | C2 | semidirect |
| 2. D4×Dic538 | C2 | semidirect |
| 3. #31770952 | C2 | semidirect |
| 4. #31770950 | C2 | semidirect |
| 5. #31770885 | C2 | semidirect |
| 6. #31770884 | C2 | semidirect |
| 7. #31770800 | C2 | semidirect |
| 8. #31770798 | C2 | semidirect |
| 9. C8×Dic538 | C2 | semidirect |
| 10. #31770685 | C2 | semidirect |
| 11. C4×D8×C269 | C2 | semidirect |
| 78. Dic538 | D8 | semidirect |
| 96. D4×C269 | #41 | semidirect |
| 131. C269 | #3358 | semidirect |
| 143. C4×D8 | D269 | semidirect |
| 222. D4 | #16864402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771276 | 2 |
| D4×Dic538 | 2 |
| #31770952 | 2 |
| #31770950 | 2 |
| #31770885 | 2 |
| #31770884 | 2 |
| #31770800 | 2 |
| #31770798 | 2 |
| C8×Dic538 | 2 |
| #31770685 | 2 |
| C4×D8×C269 | 2 |
| #3358 | 269 |