Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
456 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 4. #89956 | C2 | semidirect |
| 5. Q16×Dic7 | C2 | semidirect |
| 9. C2×C7×Q16 | C4 | semidirect |
| 69. C2×Q16 | Dic7 | semidirect |
| 132. C7 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| #90503 | 2 |
| #89997 | 2 |
| #89956 | 2 |
| Q16×Dic7 | 2 |
| #89878 | 2 |
| #89873 | 2 |
| #2950 | 7 |