Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 1. C7×#519 | C2 | semidirect |
| 3. #89999 | C2 | semidirect |
| 4. #89799 | C2 | semidirect |
| 5. #89798 | C2 | semidirect |
| 6. C4×#1143 | C2 | semidirect |
| 7. #89794 | C2 | semidirect |
| 8. #89775 | C2 | semidirect |
| 9. #89772 | C2 | semidirect |
| 65. #519 | D7 | semidirect |
| 185. C7 | #3126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#519 | 2 |
| #90226 | 2 |
| #89999 | 2 |
| #89799 | 2 |
| #89798 | 2 |
| C4×#1143 | 2 |
| #89794 | 2 |
| #89775 | 2 |
| #89772 | 2 |
| #3126 | 7 |