Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #90275 | C2 | semidirect |
| 3. C4×C7×SD16 | C2 | semidirect |
| 4. #89943 | C2 | semidirect |
| 5. #89793 | C2 | semidirect |
| 6. #89779 | C2 | semidirect |
| 7. #89632 | C2 | semidirect |
| 8. #89587 | C2 | semidirect |
| 9. #89551 | C2 | semidirect |
| 10. C8×D28 | C2 | semidirect |
| 11. #89452 | C2 | semidirect |
| 82. C4×SD16 | D7 | semidirect |
| 218. C7 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90275 | 2 |
| #90254 | 2 |
| C4×C7×SD16 | 2 |
| #89943 | 2 |
| #89793 | 2 |
| #89779 | 2 |
| #89632 | 2 |
| #89587 | 2 |
| #89551 | 2 |
| C8×D28 | 2 |
| #89452 | 2 |
| #3340 | 7 |