Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #90382 | C2 | semidirect |
| 2. C7×#499 | C2 | semidirect |
| 3. #89840 | C2 | semidirect |
| 4. #89659 | C2 | semidirect |
| 6. #89645 | C2 | semidirect |
| 7. #89644 | C2 | semidirect |
| 8. #89636 | C2 | semidirect |
| 9. #89624 | C2 | semidirect |
| 10. #89468 | C2 | semidirect |
| 11. C4×C8×D7 | C2 | semidirect |
| 73. #499 | D7 | semidirect |
| 214. C7 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90382 | 2 |
| C7×#499 | 2 |
| #89840 | 2 |
| #89659 | 2 |
| #89655 | 2 |
| #89645 | 2 |
| #89644 | 2 |
| #89636 | 2 |
| #89624 | 2 |
| #89468 | 2 |
| C4×C8×D7 | 2 |
| #3168 | 7 |