Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31771301 | C2 | semidirect |
| 2. #31771007 | C2 | semidirect |
| 3. #31770930 | C2 | semidirect |
| 4. #31770919 | C2 | semidirect |
| 5. #31770906 | C2 | semidirect |
| 6. #31770858 | C2 | semidirect |
| 7. C4×D2152 | C2 | semidirect |
| 8. #31770647 | C2 | semidirect |
| 9. #436×C269 | C2 | semidirect |
| 102. C269 | #3355 | semidirect |
| 111. #436 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771301 | 2 |
| #31771007 | 2 |
| #31770930 | 2 |
| #31770919 | 2 |
| #31770906 | 2 |
| #31770858 | 2 |
| C4×D2152 | 2 |
| #31770647 | 2 |
| #436×C269 | 2 |
| #3355 | 269 |