Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #89993 | C2 | semidirect |
| 3. C2×#6406 | C2 | semidirect |
| 4. C2×#6392 | C2 | semidirect |
| 5. C2×C8×Dic7 | C2 | semidirect |
| 9. C2×C7×D8 | C4 | semidirect |
| 66. C2×Dic7 | D8 | semidirect |
| 67. C7×C8 | C22⋊C4 | semidirect |
| 72. C2×D8 | Dic7 | semidirect |
| 147. C8 | C22⋊Dic7 | semidirect |
| 148. C7 | #1970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D8 | 2 |
| #89993 | 2 |
| C2×#6406 | 2 |
| C2×#6392 | 2 |
| C2×C8×Dic7 | 2 |
| #1970 | 7 |