Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #31770957 | C2 | semidirect |
| 3. #31770946 | C2 | semidirect |
| 4. #31770882 | C2 | semidirect |
| 5. #31770844 | C2 | semidirect |
| 6. #31770815 | C2 | semidirect |
| 7. #31770765 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. #31770599 | C2 | semidirect |
| 11. #556×C269 | C2 | semidirect |
| 125. C269 | #3302 | semidirect |
| 127. #556 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771260 | 2 |
| #31770957 | 2 |
| #31770946 | 2 |
| #31770882 | 2 |
| #31770844 | 2 |
| #31770815 | 2 |
| #31770765 | 2 |
| C4×#16864389 | 2 |
| D4×#14524130 | 2 |
| #31770599 | 2 |
| #556×C269 | 2 |
| #3302 | 269 |