Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #90161 | C2 | semidirect |
| 4. #89781 | C2 | semidirect |
| 5. #89780 | C2 | semidirect |
| 6. #89779 | C2 | semidirect |
| 7. #89736 | C2 | semidirect |
| 8. #89696 | C2 | semidirect |
| 22. #6433 | C22 | semidirect |
| 23. #6432 | C22 | semidirect |
| 24. #6432 | C22 | semidirect |
| 29. #6382 | C22 | semidirect |
| 30. #6381 | C22 | semidirect |
| 31. C4⋊(C7⋊C8) | C22 | semidirect |
| 32. C4⋊(C7⋊C8) | C22 | semidirect |
| 37. C2×C7×D4 | Q8 | semidirect |
| 148. C2×D4 | Dic14 | semidirect |
| 207. C7 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| #90161 | 2 |
| #89987 | 2 |
| #89781 | 2 |
| #89780 | 2 |
| #89779 | 2 |
| #89736 | 2 |
| #89696 | 2 |
| #3077 | 7 |