Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771328 | C2 | semidirect |
| 3. #31770955 | C2 | semidirect |
| 4. #31770945 | C2 | semidirect |
| 5. #31770886 | C2 | semidirect |
| 6. #31770843 | C2 | semidirect |
| 7. #31770766 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #31770600 | C2 | semidirect |
| 11. #462×C269 | C2 | semidirect |
| 125. C269 | #3302 | semidirect |
| 133. #462 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31771258 | 2 |
| #31770955 | 2 |
| #31770945 | 2 |
| #31770886 | 2 |
| #31770843 | 2 |
| #31770766 | 2 |
| C4×#16864389 | 2 |
| #31770670 | 2 |
| #31770600 | 2 |
| #462×C269 | 2 |
| #3302 | 269 |