Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#6433 | C2 | semidirect |
| 5. #89781 | C2 | direct (N × H) |
| 6. C2×#6382 | C2 | semidirect |
| 7. C2×#6381 | C2 | semidirect |
| 8. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 23. #6433 | C22 | semidirect |
| 26. #6382 | C22 | semidirect |
| 27. #6381 | C22 | semidirect |
| 28. C4⋊(C7⋊C8) | C22 | semidirect |
| 156. C2×C7 | #478 | semidirect |
| 185. C7 | C2×#478 | semidirect |
| 203. C2 | #89781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C2×#6433 | 2 |
| C2×#6406 | 2 |
| #89781 | 2 |
| C2×#6382 | 2 |
| C2×#6381 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C2×#478 | 7 |