Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C7×#430 | C2 | semidirect |
| 3. #89348 | C2 | semidirect |
| 4. #89290 | C2 | semidirect |
| 5. #89289 | C2 | semidirect |
| 30. #430 | D7 | semidirect |
| 96. C7 | #2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#430 | 2 |
| #89907 | 2 |
| #89348 | 2 |
| #89290 | 2 |
| #89289 | 2 |
| #2238 | 7 |