Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. #90168 | C2 | semidirect |
| 2. C2×C7×C4⋊C8 | C2 | semidirect |
| 3. #89887 | C2 | semidirect |
| 4. #89618 | C2 | semidirect |
| 5. #89615 | C2 | semidirect |
| 44. C2×C4⋊C8 | D7 | semidirect |
| 50. C2×C4×C7 | D8 | semidirect |
| 128. C2×C4 | D56 | semidirect |
| 134. C7 | #3245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90168 | 2 |
| C2×C7×C4⋊C8 | 2 |
| #89887 | 2 |
| #89618 | 2 |
| #89615 | 2 |
| #3245 | 7 |