Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C4×C7×D8 | C2 | semidirect |
| 2. C2×#6400 | C2 | semidirect |
| 3. #89467 | C2 | semidirect |
| 4. #89286 | C2 | semidirect |
| 5. C4⋊(C7⋊C16) | C2 | semidirect |
| 23. C7×D8 | D4 | semidirect |
| 35. C4×D8 | D7 | semidirect |
| 73. C4×C7 | D16 | semidirect |
| 85. D8 | D28 | semidirect |
| 113. C7 | #2206 | semidirect |
| 123. C4 | #6400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D8 | 2 |
| C2×#6400 | 2 |
| #89467 | 2 |
| #89286 | 2 |
| C4⋊(C7⋊C16) | 2 |
| #2206 | 7 |