Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 48. Dic28 | Q8 | semidirect |
| 139. C7 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90258 | 2 |
| C7×C8×Q8 | 2 |
| #89623 | 2 |
| #89601 | 2 |
| C4×Dic28 | 2 |
| #89455 | 2 |
| #89454 | 2 |
| #3383 | 7 |