Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #90270 | C2 | semidirect |
| 3. C4×C7×SD16 | C2 | semidirect |
| 4. #89945 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89780 | C2 | semidirect |
| 7. #89634 | C2 | semidirect |
| 8. #89588 | C2 | semidirect |
| 9. #89543 | C2 | semidirect |
| 10. #89460 | C2 | semidirect |
| 11. #89453 | C2 | semidirect |
| 85. C4×SD16 | D7 | semidirect |
| 230. C7 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90270 | 2 |
| #90246 | 2 |
| C4×C7×SD16 | 2 |
| #89945 | 2 |
| #89803 | 2 |
| #89780 | 2 |
| #89634 | 2 |
| #89588 | 2 |
| #89543 | 2 |
| #89460 | 2 |
| #89453 | 2 |
| #3331 | 7 |