Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #31770953 | C2 | semidirect |
| 3. #31770929 | C2 | semidirect |
| 4. #31770887 | C2 | semidirect |
| 5. #31770836 | C2 | semidirect |
| 6. #31770805 | C2 | semidirect |
| 7. #31770765 | C2 | semidirect |
| 8. C4×#16864392 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. #31770599 | C2 | semidirect |
| 11. #556×C269 | C2 | semidirect |
| 127. C269 | #3304 | semidirect |
| 129. #556 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771276 | 2 |
| #31770953 | 2 |
| #31770929 | 2 |
| #31770887 | 2 |
| #31770836 | 2 |
| #31770805 | 2 |
| #31770765 | 2 |
| C4×#16864392 | 2 |
| D4×#14524130 | 2 |
| #31770599 | 2 |
| #556×C269 | 2 |
| #3304 | 269 |