Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #90261 | C2 | semidirect |
| 3. C7×C8×Q8 | C2 | semidirect |
| 4. #89623 | C2 | semidirect |
| 7. #89453 | C2 | semidirect |
| 49. C8×Q8 | D7 | semidirect |
| 52. C7×Q8 | SD16 | semidirect |
| 121. Q8 | #1132 | semidirect |
| 133. C7 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D28 | 2 |
| #90261 | 2 |
| C7×C8×Q8 | 2 |
| #89623 | 2 |
| #89613 | 2 |
| C4×#1132 | 2 |
| #89453 | 2 |
| #3359 | 7 |