Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×C4×C7×C8 | C2 | semidirect |
| 3. #89882 | C2 | semidirect |
| 4. C2×#6393 | C2 | semidirect |
| 5. C2×#6379 | C2 | semidirect |
| 11. C2×Dic28 | C4 | semidirect |
| 14. C2×D56 | C4 | semidirect |
| 15. C2×#1132 | C4 | semidirect |
| 50. C2×C4×C8 | D7 | semidirect |
| 153. C7 | #1974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6467 | 2 |
| C2×C4×C7×C8 | 2 |
| #89882 | 2 |
| C2×#6393 | 2 |
| C2×#6379 | 2 |
| #1974 | 7 |