Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #90404 | C2 | semidirect |
| 2. #90233 | C2 | semidirect |
| 4. #89927 | C2 | semidirect |
| 5. #89925 | C2 | semidirect |
| 6. #89848 | C2 | semidirect |
| 7. C4×#1142 | C2 | semidirect |
| 8. #89621 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89539 | C2 | semidirect |
| 11. #89530 | C2 | semidirect |
| 228. C7 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90404 | 2 |
| #90233 | 2 |
| C7×#459 | 2 |
| #89927 | 2 |
| #89925 | 2 |
| #89848 | 2 |
| C4×#1142 | 2 |
| #89621 | 2 |
| #89602 | 2 |
| #89539 | 2 |
| #89530 | 2 |
| #3394 | 7 |