Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. D4×Dic14 | C2 | semidirect |
| 3. #89865 | C2 | semidirect |
| 4. #89863 | C2 | semidirect |
| 5. #89814 | C2 | semidirect |
| 6. #89812 | C2 | semidirect |
| 7. #89791 | C2 | semidirect |
| 8. C4×#1142 | C2 | semidirect |
| 9. #89784 | C2 | semidirect |
| 10. #89776 | C2 | semidirect |
| 11. #89768 | C2 | semidirect |
| 230. C7 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#555 | 2 |
| D4×Dic14 | 2 |
| #89865 | 2 |
| #89863 | 2 |
| #89814 | 2 |
| #89812 | 2 |
| #89791 | 2 |
| C4×#1142 | 2 |
| #89784 | 2 |
| #89776 | 2 |
| #89768 | 2 |
| #3329 | 7 |