Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #90421 | C2 | semidirect |
| 3. C7×#500 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89856 | C2 | semidirect |
| 6. #89660 | C2 | semidirect |
| 7. #89658 | C2 | semidirect |
| 8. #89654 | C2 | semidirect |
| 9. #89653 | C2 | semidirect |
| 10. C4×#1132 | C2 | semidirect |
| 11. #89460 | C2 | semidirect |
| 76. #500 | D7 | semidirect |
| 220. C7 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90425 | 2 |
| #90421 | 2 |
| C7×#500 | 2 |
| #89863 | 2 |
| #89856 | 2 |
| #89660 | 2 |
| #89658 | 2 |
| #89654 | 2 |
| #89653 | 2 |
| C4×#1132 | 2 |
| #89460 | 2 |
| #3357 | 7 |