Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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. C7×#568 | C2 | semidirect |
| 2. C2×#6514 | C2 | semidirect |
| 4. C2×#6472 | C2 | semidirect |
| 5. #89915 | C2 | semidirect |
| 6. #89913 | C2 | semidirect |
| 7. C2×#6398 | C2 | semidirect |
| 8. #89904 | C2 | semidirect |
| 9. #89897 | C2 | semidirect |
| 31. C2×Dic28 | C22 | semidirect |
| 32. C2×#1132 | C22 | semidirect |
| 33. #6398 | C22 | semidirect |
| 34. #6398 | C22 | semidirect |
| 35. #6397 | C22 | semidirect |
| 36. #6393 | C22 | semidirect |
| 87. #568 | D7 | semidirect |
| 263. C7 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#568 | 2 |
| C2×#6514 | 2 |
| #90513 | 2 |
| C2×#6472 | 2 |
| #89915 | 2 |
| #89913 | 2 |
| C2×#6398 | 2 |
| #89904 | 2 |
| #89897 | 2 |
| #3069 | 7 |