Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 3. C22×Dic28 | C2 | semidirect |
| 4. C2×#6450 | C2 | semidirect |
| 6. C2×Dic7⋊C8 | C2 | semidirect |
| 7. C2×#6384 | C2 | semidirect |
| 8. #89539 | C2 | direct (N × H) |
| 25. C2×Dic28 | C22 | semidirect |
| 27. #6450 | C22 | semidirect |
| 29. Dic7⋊C8 | C22 | semidirect |
| 30. #6384 | C22 | semidirect |
| 175. C2×C7 | #464 | semidirect |
| 209. C7 | C2×#464 | semidirect |
| 227. C2 | #89539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6499 | 2 |
| C22×#1142 | 2 |
| C22×Dic28 | 2 |
| C2×#6450 | 2 |
| C2×C7×#102 | 2 |
| C2×Dic7⋊C8 | 2 |
| C2×#6384 | 2 |
| #89539 | 2 |
| C2×#464 | 7 |