Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 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. #90270 | C2 | semidirect |
| 2. C7×C8×Q8 | C2 | semidirect |
| 3. #89619 | C2 | semidirect |
| 4. #89614 | C2 | semidirect |
| 7. #89455 | C2 | semidirect |
| 8. #89454 | C2 | semidirect |
| 48. D56 | Q8 | semidirect |
| 54. C8×Q8 | D7 | semidirect |
| 146. C7 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90270 | 2 |
| C7×C8×Q8 | 2 |
| #89619 | 2 |
| #89614 | 2 |
| C4×D56 | 2 |
| #89455 | 2 |
| #89454 | 2 |
| #3380 | 7 |