Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. C2×#6507 | C2 | semidirect |
| 3. C22×#1144 | C2 | semidirect |
| 6. C22×Dic28 | C2 | semidirect |
| 7. #89939 | C2 | direct (N × H) |
| 8. C2×#6389 | C2 | semidirect |
| 18. #6507 | C22 | semidirect |
| 20. C2×#1144 | C22 | semidirect |
| 29. C2×Dic28 | C22 | semidirect |
| 30. #6389 | C22 | semidirect |
| 174. C2×C7 | #497 | semidirect |
| 207. C7 | C2×#497 | semidirect |
| 222. C2 | #89939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×SD16 | 2 |
| C2×#6507 | 2 |
| C22×#1144 | 2 |
| C2×#6499 | 2 |
| C22×#1142 | 2 |
| C22×Dic28 | 2 |
| #89939 | 2 |
| C2×#6389 | 2 |
| C2×#497 | 7 |