Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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. #89862 | C2 | semidirect |
| 4. #89835 | C2 | semidirect |
| 7. #89802 | C2 | semidirect |
| 8. C4×#1144 | C2 | semidirect |
| 176. C7 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#541 | 2 |
| #90207 | 2 |
| #89862 | 2 |
| #89835 | 2 |
| #89822 | 2 |
| #89817 | 2 |
| #89802 | 2 |
| C4×#1144 | 2 |
| #89772 | 2 |
| #3127 | 7 |