Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 1. C22×C7×D8 | C2 | semidirect |
| 2. C2×#6503 | C2 | semidirect |
| 3. C22×#1141 | C2 | semidirect |
| 4. C22×D56 | C2 | semidirect |
| 5. #89923 | C2 | direct (N × H) |
| 6. C2×C8×Dic7 | C2 | semidirect |
| 11. C2×C7×D8 | C22 | semidirect |
| 14. #6503 | C22 | semidirect |
| 16. C2×#1141 | C22 | semidirect |
| 20. C2×D56 | C22 | semidirect |
| 21. C8×Dic7 | C22 | semidirect |
| 38. C2×C7×C8 | D4 | semidirect |
| 43. C2×C7⋊C8 | D4 | semidirect |
| 48. C22×D8 | D7 | semidirect |
| 67. C2×Dic7 | D8 | semidirect |
| 72. C7×C8 | C2×D4 | semidirect |
| 73. C7⋊C8 | C2×D4 | semidirect |
| 82. C2×D8 | C2×D7 | semidirect |
| 101. Dic7 | C2×D8 | semidirect |
| 121. C2×C8 | C22⋊D7 | semidirect |
| 126. C2×C7 | #493 | semidirect |
| 151. C8 | C2×C22⋊D7 | semidirect |
| 152. C7 | C2×#493 | semidirect |
| 168. C2 | #89923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D8 | 2 |
| C2×#6503 | 2 |
| C22×#1141 | 2 |
| C22×D56 | 2 |
| #89923 | 2 |
| C2×C8×Dic7 | 2 |
| C2×#493 | 7 |