Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4⋊(C7⋊C16) | C2 | semidirect |
| 4. #89256 | C2 | semidirect |
| 99. C7 | #2163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×C8 | 2 |
| C22⋊(C7⋊C16) | 2 |
| C4⋊(C7⋊C16) | 2 |
| #89256 | 2 |
| #2163 | 7 |