Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 3. C7×#477 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. C4×#1144 | C2 | semidirect |
| 6. #89658 | C2 | semidirect |
| 7. #89654 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89610 | C2 | semidirect |
| 10. #89582 | C2 | semidirect |
| 11. #89575 | C2 | semidirect |
| 81. #477 | D7 | semidirect |
| 234. C7 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90421 | 2 |
| #90268 | 2 |
| C7×#477 | 2 |
| #89860 | 2 |
| C4×#1144 | 2 |
| #89658 | 2 |
| #89654 | 2 |
| #89620 | 2 |
| #89610 | 2 |
| #89582 | 2 |
| #89575 | 2 |
| #3333 | 7 |