Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90421 | C2 | semidirect |
| 2. #90276 | C2 | semidirect |
| 3. C7×#477 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. C4×#1143 | C2 | semidirect |
| 6. #89663 | C2 | semidirect |
| 7. #89644 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89591 | C2 | semidirect |
| 11. #89572 | C2 | semidirect |
| 79. #477 | D7 | semidirect |
| 222. C7 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90421 | 2 |
| #90276 | 2 |
| C7×#477 | 2 |
| #89860 | 2 |
| C4×#1143 | 2 |
| #89663 | 2 |
| #89644 | 2 |
| #89615 | 2 |
| #89602 | 2 |
| #89591 | 2 |
| #89572 | 2 |
| #3361 | 7 |