Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #90489 | C2 | semidirect |
| 3. #89987 | C2 | semidirect |
| 4. #89924 | C2 | semidirect |
| 5. D8×Dic7 | C2 | semidirect |
| 6. #89878 | C2 | semidirect |
| 7. #89873 | C2 | semidirect |
| 9. C2×C7×D8 | C4 | semidirect |
| 15. D4×Dic7 | C22 | semidirect |
| 19. #6406 | C22 | semidirect |
| 20. #6392 | C22 | semidirect |
| 21. #6391 | C22 | semidirect |
| 22. #6389 | C22 | semidirect |
| 23. C8×Dic7 | C22 | semidirect |
| 28. C2×C7×D4 | C2×C4 | semidirect |
| 32. C7×D8 | C2×C4 | semidirect |
| 33. C7×D8 | C2×C4 | semidirect |
| 34. C2×C7×C8 | C2×C4 | semidirect |
| 71. C2×D8 | Dic7 | semidirect |
| 100. C2×D4 | C2×Dic7 | semidirect |
| 104. D8 | C2×Dic7 | semidirect |
| 105. D8 | C2×Dic7 | semidirect |
| 108. C2×C8 | C2×Dic7 | 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×C7×D8 | 2 |
| #90489 | 2 |
| #89987 | 2 |
| #89924 | 2 |
| D8×Dic7 | 2 |
| #89878 | 2 |
| #89873 | 2 |
| #2948 | 7 |