Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #90291 | C2 | semidirect |
| 3. #89927 | C2 | semidirect |
| 4. D8×Dic7 | C2 | semidirect |
| 5. #89888 | C2 | semidirect |
| 6. C2×C8×Dic7 | C2 | semidirect |
| 7. #89813 | C2 | semidirect |
| 8. #89650 | C2 | semidirect |
| 9. #89645 | C2 | semidirect |
| 10. #89540 | C2 | semidirect |
| 11. #89530 | C2 | semidirect |
| 214. C7 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90291 | 2 |
| C7×#466 | 2 |
| #89927 | 2 |
| D8×Dic7 | 2 |
| #89888 | 2 |
| C2×C8×Dic7 | 2 |
| #89813 | 2 |
| #89650 | 2 |
| #89645 | 2 |
| #89540 | 2 |
| #89530 | 2 |
| #3168 | 7 |