Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
| 4. #89873 | C2 | semidirect |
| 6. #89347 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 16. #6464 | C4 | semidirect |
| 20. #6395 | C4 | semidirect |
| 21. #6390 | C4 | semidirect |
| 24. #6379 | C4 | semidirect |
| 60. C2×C4×C8 | D7 | semidirect |
| 178. C7 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6464 | 2 |
| C2×C4×C7×C8 | 2 |
| #89885 | 2 |
| #89873 | 2 |
| C2×#6379 | 2 |
| #89347 | 2 |
| #89318 | 2 |
| #1764 | 7 |