Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90421 | C2 | semidirect |
| 2. #90404 | C2 | semidirect |
| 3. C7×#486 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 6. #89559 | C2 | semidirect |
| 7. #89540 | C2 | semidirect |
| 8. #89535 | C2 | semidirect |
| 9. #89528 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. C8×Dic14 | C2 | semidirect |
| 77. #486 | 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 |
|---|---|
| #90421 | 2 |
| #90404 | 2 |
| C7×#486 | 2 |
| #89863 | 2 |
| #89844 | 2 |
| #89559 | 2 |
| #89540 | 2 |
| #89535 | 2 |
| #89528 | 2 |
| C4×#1132 | 2 |
| C8×Dic14 | 2 |
| #3361 | 7 |