Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×C7×D8 | C2 | semidirect |
| 2. #90496 | C2 | semidirect |
| 3. #90489 | C2 | semidirect |
| 4. C2×#6495 | C2 | semidirect |
| 5. #89987 | C2 | semidirect |
| 6. #89925 | C2 | semidirect |
| 7. #89922 | C2 | semidirect |
| 8. #89885 | C2 | semidirect |
| 9. #89874 | C2 | semidirect |
| 18. #6503 | C22 | semidirect |
| 20. #6499 | C22 | semidirect |
| 22. D4×Dic7 | C22 | semidirect |
| 23. C2×#1142 | C22 | semidirect |
| 25. C2×#1141 | C22 | semidirect |
| 29. #6406 | C22 | semidirect |
| 30. #6395 | C22 | semidirect |
| 31. #6390 | C22 | semidirect |
| 32. Dic7⋊C8 | C22 | semidirect |
| 41. C2×C7×D4 | D4 | semidirect |
| 69. C22×D8 | D7 | semidirect |
| 161. C2×D4 | C22⋊D7 | semidirect |
| 219. C7 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D8 | 2 |
| #90496 | 2 |
| #90489 | 2 |
| C2×#6495 | 2 |
| #89987 | 2 |
| #89925 | 2 |
| #89922 | 2 |
| #89885 | 2 |
| #89874 | 2 |
| #3041 | 7 |