Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #90261 | C2 | semidirect |
| 3. #89865 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89841 | C2 | semidirect |
| 6. #89835 | C2 | semidirect |
| 7. #89796 | C2 | semidirect |
| 213. C7 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#554 | 2 |
| #90261 | 2 |
| #89865 | 2 |
| #89863 | 2 |
| #89841 | 2 |
| #89835 | 2 |
| #89796 | 2 |
| #89791 | 2 |
| #89790 | 2 |
| C4×#1142 | 2 |
| #3372 | 7 |