Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31771233 | C2 | semidirect |
| 3. #31770913 | C2 | semidirect |
| 4. #31770906 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770891 | C2 | semidirect |
| 7. #31770647 | C2 | semidirect |
| 8. C2×#22575385 | C2 | semidirect |
| 11. #424×C269 | C2 | semidirect |
| 42. #16864402 | Q8 | semidirect |
| 123. C269 | #3084 | semidirect |
| 133. #424 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31771085 | 2 |
| #31770913 | 2 |
| #31770906 | 2 |
| #31770896 | 2 |
| #31770891 | 2 |
| #31770647 | 2 |
| C2×#22575385 | 2 |
| #31770607 | 2 |
| #31770602 | 2 |
| #424×C269 | 2 |
| #3084 | 269 |