Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 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. C22×Dic28 | C2 | semidirect |
| 3. C2×#6374 | C2 | semidirect |
| 4. C7×C22⋊C16 | C2 | semidirect |
| 5. #89298 | C2 | semidirect |
| 33. Dic28 | D4 | semidirect |
| 40. C22⋊C16 | D7 | semidirect |
| 71. C22×C7 | SD32 | semidirect |
| 121. C7 | #2185 | semidirect |
| 127. C22 | #6374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic28 | 2 |
| #89887 | 2 |
| C2×#6374 | 2 |
| C7×C22⋊C16 | 2 |
| #89298 | 2 |
| #2185 | 7 |