Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. #90516 | C2 | semidirect |
| 3. #90489 | C2 | semidirect |
| 4. C22×#1142 | C2 | semidirect |
| 5. #90005 | C2 | semidirect |
| 6. #89934 | C2 | semidirect |
| 7. #89925 | C2 | semidirect |
| 8. #89892 | C2 | semidirect |
| 9. #89891 | C2 | semidirect |
| 18. #6507 | C22 | semidirect |
| 19. #6499 | C22 | semidirect |
| 29. #6409 | C22 | semidirect |
| 30. #6406 | C22 | semidirect |
| 31. #6390 | C22 | semidirect |
| 32. Dic7⋊C8 | C22 | semidirect |
| 212. C7 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×AGL(1,ℤ/8) | 2 |
| #90516 | 2 |
| #90489 | 2 |
| C22×#1142 | 2 |
| #90005 | 2 |
| #89934 | 2 |
| #89925 | 2 |
| #89892 | 2 |
| #89891 | 2 |
| #3042 | 7 |