Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 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 |
|---|---|---|
| 2. #89645 | C2 | semidirect |
| 4. C7×#366 | C2 | semidirect |
| 5. #89297 | C2 | semidirect |
| 6. #89287 | C2 | semidirect |
| 19. #6374 | C4 | semidirect |
| 33. Dic28 | C2×C4 | semidirect |
| 36. C7×C16 | C2×C4 | semidirect |
| 41. #366 | D7 | semidirect |
| 99. C16 | C4×D7 | semidirect |
| 119. C7 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6374 | 2 |
| #89645 | 2 |
| #89644 | 2 |
| C7×#366 | 2 |
| #89297 | 2 |
| #89287 | 2 |
| #89286 | 2 |
| #2175 | 7 |