Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#1144 | C2 | semidirect |
| 4. #90207 | C2 | semidirect |
| 6. #89997 | C2 | semidirect |
| 7. #89862 | C2 | semidirect |
| 8. #89826 | C2 | semidirect |
| 9. #89771 | C2 | semidirect |
| 205. C7 | #3044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#536 | 2 |
| C2×#6514 | 2 |
| C22×#1144 | 2 |
| #90207 | 2 |
| #90005 | 2 |
| #89997 | 2 |
| #89862 | 2 |
| #89826 | 2 |
| #89771 | 2 |
| #3044 | 7 |