Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#6478 | C2 | semidirect |
| 2. Q8×D28 | C2 | semidirect |
| 4. C4×C7×SD16 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89791 | C2 | semidirect |
| 7. #89640 | C2 | semidirect |
| 8. #89580 | C2 | semidirect |
| 9. #89555 | C2 | semidirect |
| 10. #89471 | C2 | semidirect |
| 11. #89460 | C2 | semidirect |
| 58. C7×SD16 | D4 | semidirect |
| 92. C4×SD16 | D7 | semidirect |
| 165. C4×C7 | #137 | semidirect |
| 190. SD16 | D28 | semidirect |
| 246. C7 | #3276 | semidirect |
| 261. C4 | #6478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6478 | 2 |
| Q8×D28 | 2 |
| #90246 | 2 |
| C4×C7×SD16 | 2 |
| #89803 | 2 |
| #89791 | 2 |
| #89640 | 2 |
| #89580 | 2 |
| #89555 | 2 |
| #89471 | 2 |
| #89460 | 2 |
| #3276 | 7 |