Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #31771161 | C2 | semidirect |
| 3. #31770973 | C2 | semidirect |
| 4. #31770971 | C2 | semidirect |
| 5. #31770970 | C2 | semidirect |
| 6. #31770966 | C2 | semidirect |
| 7. #31770600 | C2 | semidirect |
| 8. #97×D269 | C2 | semidirect |
| 9. #491×C269 | C2 | semidirect |
| 90. C269 | #3135 | semidirect |
| 95. #491 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771161 | 2 |
| #31771156 | 2 |
| #31770973 | 2 |
| #31770971 | 2 |
| #31770970 | 2 |
| #31770966 | 2 |
| #31770600 | 2 |
| #97×D269 | 2 |
| #491×C269 | 2 |
| #3135 | 269 |