Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic28 | C2 | semidirect |
| 4. #89888 | C2 | semidirect |
| 5. #89621 | C2 | semidirect |
| 6. #89511 | C2 | semidirect |
| 7. #89471 | C2 | semidirect |
| 8. C4×Dic28 | C2 | semidirect |
| 55. Dic28 | D4 | direct (N × H) |
| 65. C7×D4 | Q16 | semidirect |
| 106. C22×C7 | C2×Q16 | semidirect |
| 110. C4×C7 | C2×Q16 | semidirect |
| 152. D4 | Dic28 | direct (N × H) |
| 166. C7 | D4×Q16 | semidirect |
| 169. C22 | C2×Dic28 | semidirect |
| 176. C4 | C2×Dic28 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic28 | 2 |
| D4×Dic14 | 2 |
| C7×C8×D4 | 2 |
| #89888 | 2 |
| #89621 | 2 |
| #89511 | 2 |
| #89471 | 2 |
| C4×Dic28 | 2 |
| D4×Q16 | 7 |