Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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×Q8×Dic7 | C2 | semidirect |
| 3. C22×#1144 | C2 | semidirect |
| 6. #89938 | C2 | direct (N × H) |
| 7. C2×#6390 | C2 | semidirect |
| 8. C2×Dic7⋊C8 | C2 | semidirect |
| 18. Q8×Dic7 | C22 | semidirect |
| 20. C2×#1144 | C22 | semidirect |
| 29. #6390 | C22 | semidirect |
| 30. Dic7⋊C8 | C22 | semidirect |
| 175. C2×C7 | #464 | semidirect |
| 209. C7 | C2×#464 | semidirect |
| 227. C2 | #89938 | 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×Q8×Dic7 | 2 |
| C22×#1144 | 2 |
| C2×#6499 | 2 |
| C2×#6406 | 2 |
| #89938 | 2 |
| C2×#6390 | 2 |
| C2×Dic7⋊C8 | 2 |
| C2×#464 | 7 |