Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #90210 | C2 | semidirect |
| 3. C7×#424 | C2 | semidirect |
| 5. #89893 | C2 | semidirect |
| 7. #89878 | C2 | semidirect |
| 8. #89619 | C2 | semidirect |
| 9. #89619 | C2 | semidirect |
| 10. #89618 | C2 | semidirect |
| 11. #89614 | C2 | semidirect |
| 27. #6433 | C22 | semidirect |
| 28. #6432 | C22 | semidirect |
| 29. C7×C4⋊C8 | C22 | semidirect |
| 30. C7×C4⋊C8 | C22 | semidirect |
| 35. #6392 | C22 | semidirect |
| 36. #6392 | C22 | semidirect |
| 37. #6392 | C22 | semidirect |
| 38. #6391 | C22 | semidirect |
| 39. #6391 | C22 | semidirect |
| 40. #6391 | C22 | semidirect |
| 47. C2×D28 | Q8 | semidirect |
| 84. #424 | D7 | semidirect |
| 136. C4⋊C8 | C2×D7 | semidirect |
| 137. C4⋊C8 | C2×D7 | semidirect |
| 225. C7 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90212 | 2 |
| #90210 | 2 |
| C7×#424 | 2 |
| #89903 | 2 |
| #89893 | 2 |
| C2×#6395 | 2 |
| #89878 | 2 |
| #89619 | 2 |
| #89618 | 2 |
| #89614 | 2 |
| #3081 | 7 |