Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31771156 | C2 | semidirect |
| 2. C4×#16864403 | C2 | semidirect |
| 3. #31770931 | C2 | semidirect |
| 4. #31770882 | C2 | semidirect |
| 5. #31770805 | C2 | semidirect |
| 6. #31770801 | C2 | semidirect |
| 7. #31770753 | C2 | semidirect |
| 8. #31770716 | C2 | semidirect |
| 9. #31770708 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 93. D1076 | #41 | semidirect |
| 109. Q8×C269 | #41 | semidirect |
| 144. C269 | #3115 | semidirect |
| 149. #475 | D269 | semidirect |
| 233. Q8 | #16864403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| C4×#16864403 | 2 |
| #31770931 | 2 |
| #31770882 | 2 |
| #31770805 | 2 |
| #31770801 | 2 |
| #31770753 | 2 |
| #31770716 | 2 |
| #31770708 | 2 |
| #31770661 | 2 |
| #475×C269 | 2 |
| #3115 | 269 |