Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
256 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 79 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×#6381 | C2 | semidirect |
| 5. C7×#340 | C2 | semidirect |
| 6. #89346 | C2 | semidirect |
| 7. #89324 | C2 | semidirect |
| 57. #340 | D7 | semidirect |
| 201. C7 | #2075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×D7)⋊C8 | 2 |
| #89759 | 2 |
| C2×#6381 | 2 |
| C7×#340 | 2 |
| #89346 | 2 |
| #89324 | 2 |
| #2075 | 7 |