Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771340 | C2 | semidirect |
| 2. D4×Dic538 | C2 | semidirect |
| 3. #31770966 | C2 | semidirect |
| 4. #31770952 | C2 | semidirect |
| 5. #31770894 | C2 | semidirect |
| 6. #31770890 | C2 | semidirect |
| 7. #31770822 | C2 | semidirect |
| 9. #31770735 | C2 | semidirect |
| 10. #31770714 | C2 | semidirect |
| 11. C4×SD16×C269 | C2 | semidirect |
| 124. C269 | #3373 | semidirect |
| 136. C4×SD16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771340 | 2 |
| D4×Dic538 | 2 |
| #31770966 | 2 |
| #31770952 | 2 |
| #31770894 | 2 |
| #31770890 | 2 |
| #31770822 | 2 |
| #31770800 | 2 |
| #31770735 | 2 |
| #31770714 | 2 |
| C4×SD16×C269 | 2 |
| #3373 | 269 |