Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #90214 | C2 | semidirect |
| 3. C7×#418 | C2 | semidirect |
| 4. C2×#6406 | C2 | semidirect |
| 5. #89901 | C2 | semidirect |
| 6. #89893 | C2 | semidirect |
| 7. #89770 | C2 | semidirect |
| 8. #89556 | C2 | semidirect |
| 9. #89551 | C2 | semidirect |
| 10. #89549 | C2 | semidirect |
| 11. #89546 | C2 | semidirect |
| 24. #6455 | C22 | semidirect |
| 25. D7×C4⋊C4 | C22 | semidirect |
| 33. (C2×D7)⋊C8 | C22 | semidirect |
| 34. (C2×D7)⋊C8 | C22 | semidirect |
| 35. #6392 | C22 | semidirect |
| 36. #6391 | C22 | semidirect |
| 37. #6382 | C22 | semidirect |
| 38. #6382 | C22 | semidirect |
| 39. #6381 | C22 | semidirect |
| 40. #6381 | C22 | semidirect |
| 86. #418 | D7 | semidirect |
| 242. C7 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90496 | 2 |
| #90214 | 2 |
| C7×#418 | 2 |
| C2×#6406 | 2 |
| #89901 | 2 |
| #89893 | 2 |
| #89770 | 2 |
| #89556 | 2 |
| #89551 | 2 |
| #89549 | 2 |
| #89546 | 2 |
| #3096 | 7 |