Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 4. #31770887 | C2 | semidirect |
| 5. #31770816 | C2 | semidirect |
| 6. #31770815 | C2 | semidirect |
| 8. #31770711 | C2 | semidirect |
| 9. #31770709 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 132. C269 | #3113 | semidirect |
| 138. #475 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| C4×Q8×D269 | 2 |
| #31770937 | 2 |
| #31770887 | 2 |
| #31770816 | 2 |
| #31770815 | 2 |
| #31770762 | 2 |
| #31770711 | 2 |
| #31770709 | 2 |
| #31770661 | 2 |
| #475×C269 | 2 |
| #3113 | 269 |