Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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×#533 | C2 | semidirect |
| 5. #89328 | C2 | semidirect |
| 6. #89326 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 32. C2×D28 | Q8 | semidirect |
| 34. C2×Dic14 | Q8 | semidirect |
| 55. #533 | D7 | semidirect |
| 181. C7 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#533 | 2 |
| #89778 | 2 |
| #89777 | 2 |
| C2×#6379 | 2 |
| #89328 | 2 |
| #89326 | 2 |
| #89318 | 2 |
| #2031 | 7 |