Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D269 | C2 | semidirect |
| 3. #31770898 | C2 | semidirect |
| 4. #31770894 | C2 | semidirect |
| 5. #31770890 | C2 | semidirect |
| 6. #31770886 | C2 | semidirect |
| 7. #31770882 | C2 | semidirect |
| 8. #31770644 | C2 | semidirect |
| 9. #31770627 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 44. #16864403 | Q8 | semidirect |
| 88. D1076 | C2×Q8 | semidirect |
| 105. Q8×C269 | C2×Q8 | semidirect |
| 137. C269 | #3079 | semidirect |
| 144. #475 | D269 | semidirect |
| 226. Q8 | Q8×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D269 | 2 |
| C4×#16864403 | 2 |
| #31770898 | 2 |
| #31770894 | 2 |
| #31770890 | 2 |
| #31770886 | 2 |
| #31770882 | 2 |
| #31770644 | 2 |
| #31770627 | 2 |
| #31770605 | 2 |
| #475×C269 | 2 |
| #3079 | 269 |