Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 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×#544 | C2 | semidirect |
| 4. #89333 | C2 | semidirect |
| 5. #89323 | C2 | semidirect |
| 42. #544 | D7 | semidirect |
| 64. C2×C4×C7 | SD16 | semidirect |
| 153. C2×C4 | #1143 | semidirect |
| 156. C7 | #1599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#544 | 2 |
| #89818 | 2 |
| #89763 | 2 |
| #89333 | 2 |
| #89323 | 2 |
| #1599 | 7 |