Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
292 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C4×C7×C8 | C2 | semidirect |
| 4. C2×Dic7⋊C8 | C2 | semidirect |
| 6. #89345 | C2 | semidirect |
| 7. #89319 | C2 | semidirect |
| 46. (C2×D7)⋊C4 | C8 | semidirect |
| 58. C2×C4×C8 | D7 | semidirect |
| 213. C7 | #1923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×C8 | 2 |
| C2×(C2×D7)⋊C8 | 2 |
| C2×Dic7⋊C8 | 2 |
| C4×(C2×D7)⋊C4 | 2 |
| #89345 | 2 |
| #89319 | 2 |
| #1923 | 7 |