Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #31770915 | C2 | semidirect |
| 4. #31770914 | C2 | semidirect |
| 5. #31770901 | C2 | semidirect |
| 6. #31770900 | C2 | semidirect |
| 7. #31770887 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 47. Q8×D269 | Q8 | semidirect |
| 130. C269 | #3078 | semidirect |
| 139. #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 |
| #31770915 | 2 |
| #31770914 | 2 |
| #31770901 | 2 |
| #31770900 | 2 |
| #31770887 | 2 |
| #31770644 | 2 |
| #31770627 | 2 |
| #31770612 | 2 |
| #475×C269 | 2 |
| #3078 | 269 |