Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. #90168 | C2 | semidirect |
| 2. C2×C4×D28 | C2 | semidirect |
| 3. C7×#431 | C2 | semidirect |
| 4. #89618 | C2 | semidirect |
| 5. #89615 | C2 | semidirect |
| 6. #89508 | C2 | semidirect |
| 7. #89504 | C2 | semidirect |
| 8. C4×D56 | C2 | semidirect |
| 19. #6437 | C22 | semidirect |
| 25. C4×D28 | C22 | semidirect |
| 26. #6432 | C22 | semidirect |
| 27. C7×C4⋊C8 | C22 | semidirect |
| 29. C4×C7×C8 | C22 | semidirect |
| 31. #6395 | C22 | semidirect |
| 32. #6392 | C22 | semidirect |
| 73. #431 | D7 | semidirect |
| 82. C2×C4×C7 | D8 | semidirect |
| 98. D28 | #41 | semidirect |
| 123. C4⋊C8 | C2×D7 | semidirect |
| 127. C4×C8 | C2×D7 | semidirect |
| 207. C2×C4 | D56 | semidirect |
| 215. C7 | #3100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90168 | 2 |
| C2×C4×D28 | 2 |
| C7×#431 | 2 |
| #89618 | 2 |
| #89615 | 2 |
| #89508 | 2 |
| #89504 | 2 |
| C4×D56 | 2 |
| #3100 | 7 |