Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31770887 | C2 | semidirect |
| 3. C8×Dic538 | C2 | semidirect |
| 4. #31770356 | C2 | semidirect |
| 5. #31770351 | C2 | semidirect |
| 43. Dic538 | SD16 | semidirect |
| 62. C8×C269 | SD16 | semidirect |
| 79. C269 | #1666 | semidirect |
| 142. C8 | #16864390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770887 | 2 |
| #31770802 | 2 |
| C8×Dic538 | 2 |
| #31770356 | 2 |
| #31770351 | 2 |
| #31770349 | 2 |
| #492×C269 | 2 |
| #1666 | 269 |