Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #90268 | C2 | semidirect |
| 2. C7×C8×Q8 | C2 | semidirect |
| 3. #89615 | C2 | semidirect |
| 4. #89467 | C2 | semidirect |
| 5. C4×D56 | C2 | semidirect |
| 35. C8×Q8 | D7 | semidirect |
| 38. C7×Q8 | D8 | semidirect |
| 49. C7×C8 | #41 | semidirect |
| 89. Q8 | D56 | semidirect |
| 100. C8 | #1161 | semidirect |
| 101. C7 | #3391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90268 | 2 |
| C7×C8×Q8 | 2 |
| #89615 | 2 |
| #89467 | 2 |
| C4×D56 | 2 |
| #3391 | 7 |