Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic7 | C2 | semidirect |
| 3. #90004 | C2 | semidirect |
| 4. #89979 | C2 | semidirect |
| 5. #89816 | C2 | semidirect |
| 6. #89815 | C2 | semidirect |
| 7. #89806 | C2 | semidirect |
| 8. #89805 | C2 | semidirect |
| 9. #89767 | C2 | semidirect |
| 29. #6409 | C22 | semidirect |
| 30. #6406 | C22 | semidirect |
| 33. #6382 | C22 | semidirect |
| 34. #6381 | C22 | semidirect |
| 231. C7 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#525 | 2 |
| C22×C4⋊Dic7 | 2 |
| #90004 | 2 |
| #89979 | 2 |
| #89816 | 2 |
| #89815 | 2 |
| #89806 | 2 |
| #89805 | 2 |
| #89767 | 2 |
| #3092 | 7 |