Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. #90161 | C2 | semidirect |
| 3. C7×#431 | C2 | semidirect |
| 4. #89623 | C2 | semidirect |
| 5. #89621 | C2 | semidirect |
| 6. #89618 | C2 | semidirect |
| 7. #89613 | C2 | semidirect |
| 9. #89495 | C2 | semidirect |
| 10. C4×Dic28 | C2 | semidirect |
| 11. C4×#1132 | C2 | semidirect |
| 93. #431 | D7 | semidirect |
| 248. C7 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#1157 | 2 |
| #90161 | 2 |
| C7×#431 | 2 |
| #89623 | 2 |
| #89621 | 2 |
| #89618 | 2 |
| #89613 | 2 |
| #89505 | 2 |
| #89495 | 2 |
| C4×Dic28 | 2 |
| C4×#1132 | 2 |
| #3107 | 7 |