Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771329 | C2 | semidirect |
| 3. #31770942 | C2 | semidirect |
| 4. #31770932 | C2 | semidirect |
| 5. #31770887 | C2 | semidirect |
| 6. #31770882 | C2 | semidirect |
| 7. #31770852 | C2 | semidirect |
| 8. C4×#16864391 | C2 | semidirect |
| 9. #31770684 | C2 | semidirect |
| 10. #31770646 | C2 | semidirect |
| 11. #500×C269 | C2 | semidirect |
| 99. C8×C269 | #41 | semidirect |
| 122. C269 | #3353 | semidirect |
| 126. #500 | D269 | semidirect |
| 222. C8 | #16864403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771329 | 2 |
| #31771258 | 2 |
| #31770942 | 2 |
| #31770932 | 2 |
| #31770887 | 2 |
| #31770882 | 2 |
| #31770852 | 2 |
| C4×#16864391 | 2 |
| #31770684 | 2 |
| #31770646 | 2 |
| #500×C269 | 2 |
| #3353 | 269 |