Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#6479 | C2 | semidirect |
| 2. #90268 | C2 | semidirect |
| 3. #90246 | C2 | semidirect |
| 4. C4×C7×SD16 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89787 | C2 | semidirect |
| 7. #89636 | C2 | semidirect |
| 8. #89582 | C2 | semidirect |
| 9. #89553 | C2 | semidirect |
| 10. #89465 | C2 | semidirect |
| 11. C8×D28 | C2 | semidirect |
| 61. C7×SD16 | D4 | semidirect |
| 92. C4×SD16 | D7 | semidirect |
| 171. C4×C7 | #135 | semidirect |
| 197. SD16 | D28 | semidirect |
| 255. C7 | #3284 | semidirect |
| 272. C4 | #6479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6479 | 2 |
| #90268 | 2 |
| #90246 | 2 |
| C4×C7×SD16 | 2 |
| #89803 | 2 |
| #89787 | 2 |
| #89636 | 2 |
| #89582 | 2 |
| #89553 | 2 |
| #89465 | 2 |
| C8×D28 | 2 |
| #3284 | 7 |