Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90248 | C2 | semidirect |
| 2. C7×#442 | C2 | semidirect |
| 4. #89927 | C2 | semidirect |
| 5. #89790 | C2 | semidirect |
| 6. #89640 | C2 | semidirect |
| 7. #89630 | C2 | semidirect |
| 8. #89552 | C2 | semidirect |
| 9. #89540 | C2 | semidirect |
| 10. #89488 | C2 | semidirect |
| 11. #89479 | C2 | semidirect |
| 77. #442 | D7 | semidirect |
| 200. C7 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90248 | 2 |
| C7×#442 | 2 |
| #89931 | 2 |
| #89927 | 2 |
| #89790 | 2 |
| #89640 | 2 |
| #89630 | 2 |
| #89552 | 2 |
| #89540 | 2 |
| #89488 | 2 |
| #89479 | 2 |
| #3183 | 7 |