Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#6432 | C2 | semidirect |
| 4. C7×#336 | C2 | semidirect |
| 5. #89346 | C2 | semidirect |
| 27. C2×D28 | Q8 | semidirect |
| 45. #336 | D7 | semidirect |
| 164. C7 | #2023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6432 | 2 |
| C2×#6395 | 2 |
| #89711 | 2 |
| C7×#336 | 2 |
| #89346 | 2 |
| #2023 | 7 |