Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 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. #31771325 | C2 | semidirect |
| 2. D4×Dic538 | C2 | semidirect |
| 3. #31770963 | C2 | semidirect |
| 4. #31770956 | C2 | semidirect |
| 5. #31770899 | C2 | semidirect |
| 6. #31770885 | C2 | semidirect |
| 8. #31770810 | C2 | semidirect |
| 9. #31770735 | C2 | semidirect |
| 10. #31770702 | C2 | semidirect |
| 122. C269 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771325 | 2 |
| D4×Dic538 | 2 |
| #31770963 | 2 |
| #31770956 | 2 |
| #31770899 | 2 |
| #31770885 | 2 |
| #31770818 | 2 |
| #31770810 | 2 |
| #31770735 | 2 |
| #31770702 | 2 |
| C4×D8×C269 | 2 |
| #3367 | 269 |