Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #90212 | C2 | semidirect |
| 3. C7×#427 | C2 | semidirect |
| 4. #89873 | C2 | semidirect |
| 5. #89773 | C2 | semidirect |
| 6. #89644 | C2 | semidirect |
| 7. #89641 | C2 | semidirect |
| 13. C2×D56 | C4 | semidirect |
| 16. #6456 | C22 | semidirect |
| 19. C7×#107 | C22 | semidirect |
| 20. C7×#106 | C22 | semidirect |
| 21. #6389 | C22 | semidirect |
| 22. C8×Dic7 | C22 | semidirect |
| 23. #6383 | C22 | semidirect |
| 29. C2×D28 | C2×C4 | semidirect |
| 32. C2×C7×C8 | C2×C4 | semidirect |
| 44. D56 | C2×C4 | semidirect |
| 45. D56 | C2×C4 | semidirect |
| 50. #427 | D7 | semidirect |
| 81. #107 | C2×D7 | semidirect |
| 82. #106 | C2×D7 | semidirect |
| 108. C2×C8 | C4×D7 | semidirect |
| 139. C7 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D56 | 2 |
| #90212 | 2 |
| C7×#427 | 2 |
| #89873 | 2 |
| #89773 | 2 |
| #89644 | 2 |
| #89641 | 2 |
| #2948 | 7 |