Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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. #90276 | C2 | semidirect |
| 2. #90270 | C2 | semidirect |
| 3. C7×C8×Q8 | C2 | semidirect |
| 4. #89622 | C2 | semidirect |
| 5. #89619 | C2 | semidirect |
| 6. #89616 | C2 | semidirect |
| 8. #89469 | C2 | semidirect |
| 9. #89466 | C2 | semidirect |
| 10. C4×D56 | C2 | semidirect |
| 11. C4×#1132 | C2 | semidirect |
| 82. C8×Q8 | D7 | semidirect |
| 222. C7 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90276 | 2 |
| #90270 | 2 |
| C7×C8×Q8 | 2 |
| #89622 | 2 |
| #89619 | 2 |
| #89616 | 2 |
| #89615 | 2 |
| #89469 | 2 |
| #89466 | 2 |
| C4×D56 | 2 |
| C4×#1132 | 2 |
| #3361 | 7 |