Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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. C7×C8×Q8 | C2 | semidirect |
| 3. Q8×C7⋊C8 | C2 | semidirect |
| 5. #89603 | C2 | semidirect |
| 7. #89451 | C2 | semidirect |
| 46. C8×Q8 | D7 | semidirect |
| 131. C7 | #2984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D7 | 2 |
| C7×C8×Q8 | 2 |
| Q8×C7⋊C8 | 2 |
| #89607 | 2 |
| #89603 | 2 |
| #89457 | 2 |
| #89451 | 2 |
| #2984 | 7 |