Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31770909 | C2 | semidirect |
| 3. #31770902 | C2 | semidirect |
| 4. #31770897 | C2 | semidirect |
| 5. #31770882 | C2 | semidirect |
| 6. #31770648 | C2 | semidirect |
| 7. C2×#22575386 | C2 | semidirect |
| 8. #31770632 | C2 | semidirect |
| 11. #544×C269 | C2 | semidirect |
| 42. #16864402 | Q8 | semidirect |
| 123. C269 | #3083 | semidirect |
| 125. #544 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771085 | 2 |
| #31770909 | 2 |
| #31770902 | 2 |
| #31770897 | 2 |
| #31770882 | 2 |
| #31770648 | 2 |
| C2×#22575386 | 2 |
| #31770632 | 2 |
| #31770604 | 2 |
| #31770599 | 2 |
| #544×C269 | 2 |
| #3083 | 269 |