Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31771139 | C2 | semidirect |
| 2. #31770905 | C2 | semidirect |
| 3. #31770887 | C2 | semidirect |
| 4. #31770882 | C2 | semidirect |
| 5. #31770856 | C2 | semidirect |
| 6. #31770849 | C2 | semidirect |
| 7. #31770820 | C2 | semidirect |
| 8. #31770802 | C2 | semidirect |
| 9. #31770797 | C2 | semidirect |
| 10. #31770629 | C2 | semidirect |
| 11. #532×C269 | C2 | semidirect |
| 141. C269 | #3251 | semidirect |
| 143. #532 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| #31770905 | 2 |
| #31770887 | 2 |
| #31770882 | 2 |
| #31770856 | 2 |
| #31770849 | 2 |
| #31770820 | 2 |
| #31770802 | 2 |
| #31770797 | 2 |
| #31770629 | 2 |
| #532×C269 | 2 |
| #3251 | 269 |