Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×C7×D8 | C2 | semidirect |
| 3. C4×D56 | C2 | semidirect |
| 4. #89357 | C2 | semidirect |
| 5. #89286 | C2 | semidirect |
| 6. #89285 | C2 | semidirect |
| 7. #89256 | C2 | semidirect |
| 15. #6400 | C4 | semidirect |
| 26. C7×D8 | C2×C4 | semidirect |
| 35. D56 | C2×C4 | semidirect |
| 37. C7⋊C16 | C2×C4 | semidirect |
| 40. C4×D8 | D7 | semidirect |
| 93. D8 | C4×D7 | semidirect |
| 124. C7 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D8 | 2 |
| C2×#6400 | 2 |
| C4×D56 | 2 |
| #89357 | 2 |
| #89286 | 2 |
| #89285 | 2 |
| #89256 | 2 |
| #2177 | 7 |