Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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. #89698 | C2 | semidirect |
| 4. #89254 | C2 | semidirect |
| 5. #89251 | C2 | semidirect |
| 52. C2×C4×C8 | D7 | semidirect |
| 159. C7 | #1494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90170 | 2 |
| C2×C4×C7×C8 | 2 |
| #89698 | 2 |
| #89254 | 2 |
| #89251 | 2 |
| #1494 | 7 |