Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. C7×#492 | C2 | semidirect |
| 2. #89859 | C2 | semidirect |
| 4. C8×D28 | C2 | semidirect |
| 5. #89342 | C2 | semidirect |
| 6. #89339 | C2 | semidirect |
| 7. #89252 | C2 | semidirect |
| 44. #492 | D7 | semidirect |
| 66. D28 | SD16 | semidirect |
| 70. C7×C8 | D8 | semidirect |
| 150. C8 | #1141 | semidirect |
| 151. C7 | #1665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#492 | 2 |
| #89859 | 2 |
| #89844 | 2 |
| C8×D28 | 2 |
| #89342 | 2 |
| #89339 | 2 |
| #89252 | 2 |
| #1665 | 7 |