Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #90000 | C2 | semidirect |
| 4. #89997 | C2 | semidirect |
| 5. #89862 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 7. #89824 | C2 | semidirect |
| 8. #89817 | C2 | semidirect |
| 9. C4×#1144 | C2 | semidirect |
| 10. #89792 | C2 | semidirect |
| 223. C7 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Q8 | 2 |
| #90233 | 2 |
| #90000 | 2 |
| #89997 | 2 |
| #89862 | 2 |
| #89853 | 2 |
| #89824 | 2 |
| #89817 | 2 |
| C4×#1144 | 2 |
| #89792 | 2 |
| #89784 | 2 |
| #3328 | 7 |