Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 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 |
|---|---|---|
| 4. #89803 | C2 | semidirect |
| 5. #89802 | C2 | semidirect |
| 6. C4×#1144 | C2 | semidirect |
| 7. #89794 | 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×#519 | 2 |
| #90209 | 2 |
| #90000 | 2 |
| #89803 | 2 |
| #89802 | 2 |
| C4×#1144 | 2 |
| #89794 | 2 |
| #89772 | 2 |
| #89768 | 2 |
| #3127 | 7 |