Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #31771328 | C2 | semidirect |
| 2. #31770967 | C2 | semidirect |
| 3. #31770957 | C2 | semidirect |
| 4. #31770897 | C2 | semidirect |
| 5. #31770882 | C2 | semidirect |
| 7. #31770810 | C2 | semidirect |
| 8. #31770736 | C2 | semidirect |
| 9. #31770705 | C2 | semidirect |
| 11. D4×Q8×C269 | C2 | semidirect |
| 122. C269 | #3367 | semidirect |
| 125. D4×Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31770967 | 2 |
| #31770957 | 2 |
| #31770897 | 2 |
| #31770882 | 2 |
| #31770820 | 2 |
| #31770810 | 2 |
| #31770736 | 2 |
| #31770705 | 2 |
| C4×#16864387 | 2 |
| D4×Q8×C269 | 2 |
| #3367 | 269 |