Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 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×#446 | C2 | semidirect |
| 2. #89799 | C2 | semidirect |
| 4. #89280 | C2 | semidirect |
| 5. #89252 | C2 | semidirect |
| 35. #446 | D7 | semidirect |
| 52. C7×C8 | SD16 | semidirect |
| 109. C8 | #1143 | semidirect |
| 110. C7 | #1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#446 | 2 |
| #89799 | 2 |
| #89467 | 2 |
| #89280 | 2 |
| #89252 | 2 |
| #1688 | 7 |