Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #89892 | C2 | semidirect |
| 5. #89776 | C2 | semidirect |
| 6. C7×#339 | C2 | semidirect |
| 7. #89318 | C2 | semidirect |
| 19. #6438 | C4 | semidirect |
| 41. C2×Dic14 | C2×C4 | semidirect |
| 49. C42×C7 | C2×C4 | semidirect |
| 64. #339 | D7 | semidirect |
| 158. C42 | C4×D7 | semidirect |
| 193. C7 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90212 | 2 |
| C2×#6438 | 2 |
| C2×#6397 | 2 |
| #89892 | 2 |
| #89776 | 2 |
| C7×#339 | 2 |
| #89318 | 2 |
| #1885 | 7 |