Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31771233 | C2 | semidirect |
| 3. #31770915 | C2 | semidirect |
| 4. #31770904 | C2 | semidirect |
| 5. #31770899 | C2 | semidirect |
| 6. #31770884 | C2 | semidirect |
| 7. C2×#22575386 | C2 | semidirect |
| 8. #31770633 | C2 | semidirect |
| 11. #428×C269 | C2 | semidirect |
| 42. #16864402 | Q8 | semidirect |
| 123. C269 | #3083 | semidirect |
| 131. #428 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31771086 | 2 |
| #31770915 | 2 |
| #31770904 | 2 |
| #31770899 | 2 |
| #31770884 | 2 |
| C2×#22575386 | 2 |
| #31770633 | 2 |
| #31770607 | 2 |
| #31770599 | 2 |
| #428×C269 | 2 |
| #3083 | 269 |