Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. Q8×D1076 | C2 | semidirect |
| 2. #31770964 | C2 | semidirect |
| 3. #31770955 | C2 | semidirect |
| 4. #31770900 | C2 | semidirect |
| 5. #31770885 | C2 | semidirect |
| 7. #31770807 | C2 | semidirect |
| 8. #31770736 | C2 | semidirect |
| 9. #31770703 | C2 | semidirect |
| 11. #556×C269 | C2 | semidirect |
| 122. C269 | #3367 | semidirect |
| 124. #556 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1076 | 2 |
| #31770964 | 2 |
| #31770955 | 2 |
| #31770900 | 2 |
| #31770885 | 2 |
| #31770817 | 2 |
| #31770807 | 2 |
| #31770736 | 2 |
| #31770703 | 2 |
| C4×#16864387 | 2 |
| #556×C269 | 2 |
| #3367 | 269 |