Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #31770561 | C2 | semidirect |
| 5. #31770374 | C2 | semidirect |
| 6. #31770369 | C2 | semidirect |
| 7. #428×C269 | C2 | semidirect |
| 16. #22575369 | C4 | semidirect |
| 100. C269 | #1931 | semidirect |
| 102. #428 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770609 | 2 |
| C2×#22575373 | 2 |
| C2×#22575369 | 2 |
| #31770561 | 2 |
| #31770374 | 2 |
| #31770369 | 2 |
| #428×C269 | 2 |
| #1931 | 269 |