Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 4. #89471 | C2 | semidirect |
| 5. C4×Dic28 | C2 | semidirect |
| 6. #89454 | C2 | semidirect |
| 7. #89453 | C2 | semidirect |
| 56. C2×C4×C7 | Q16 | semidirect |
| 129. C2×C4 | Dic28 | semidirect |
| 138. C7 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90161 | 2 |
| C2×C4×C7×C8 | 2 |
| #89888 | 2 |
| #89471 | 2 |
| C4×Dic28 | 2 |
| #89454 | 2 |
| #89453 | 2 |
| #3170 | 7 |