Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Dic7⋊C8 | C2 | semidirect |
| 5. #89345 | C2 | semidirect |
| 33. C22⋊Dic7 | C8 | semidirect |
| 65. C2×Dic7 | C2×C8 | semidirect |
| 85. C22×C7 | C4⋊C8 | semidirect |
| 148. C7 | #1850 | semidirect |
| 153. C22 | Dic7⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C8 | 2 |
| C4×C22⋊Dic7 | 2 |
| C2×C22⋊(C7⋊C8) | 2 |
| C2×Dic7⋊C8 | 2 |
| #89345 | 2 |
| #1850 | 7 |