Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771315 | C2 | semidirect |
| 2. #31771277 | C2 | semidirect |
| 3. #31770970 | C2 | semidirect |
| 4. #31770952 | C2 | semidirect |
| 5. #31770906 | C2 | semidirect |
| 6. #31770896 | C2 | semidirect |
| 7. #31770801 | C2 | semidirect |
| 8. #31770801 | C2 | semidirect |
| 9. #31770718 | C2 | semidirect |
| 10. C4×D2152 | C2 | semidirect |
| 11. #446×C269 | C2 | semidirect |
| 87. D1076 | #41 | semidirect |
| 129. C269 | #3366 | semidirect |
| 139. #446 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771315 | 2 |
| #31771277 | 2 |
| #31770970 | 2 |
| #31770952 | 2 |
| #31770906 | 2 |
| #31770896 | 2 |
| #31770801 | 2 |
| #31770718 | 2 |
| C4×D2152 | 2 |
| #446×C269 | 2 |
| #3366 | 269 |