Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#6481 | C2 | semidirect |
| 3. Q8×D28 | C2 | semidirect |
| 4. C4×C7×Q16 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89799 | C2 | semidirect |
| 7. #89658 | C2 | semidirect |
| 8. #89582 | C2 | semidirect |
| 9. #89578 | C2 | semidirect |
| 10. #89465 | C2 | semidirect |
| 11. #89460 | C2 | semidirect |
| 60. C7×Q16 | D4 | semidirect |
| 92. C4×Q16 | D7 | semidirect |
| 168. C4×C7 | #137 | semidirect |
| 191. Q16 | D28 | semidirect |
| 250. C7 | #3278 | semidirect |
| 265. C4 | #6481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6481 | 2 |
| #90268 | 2 |
| Q8×D28 | 2 |
| C4×C7×Q16 | 2 |
| #89803 | 2 |
| #89799 | 2 |
| #89658 | 2 |
| #89582 | 2 |
| #89578 | 2 |
| #89465 | 2 |
| #89460 | 2 |
| #3278 | 7 |