Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #90419 | C2 | semidirect |
| 3. C7×#475 | C2 | semidirect |
| 4. #89859 | C2 | semidirect |
| 5. #89803 | C2 | semidirect |
| 6. #89639 | C2 | semidirect |
| 7. #89624 | C2 | semidirect |
| 8. #89613 | C2 | semidirect |
| 9. #89605 | C2 | semidirect |
| 11. #89562 | C2 | semidirect |
| 86. #475 | D7 | semidirect |
| 248. C7 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| C4×#1161 | 2 |
| C7×#475 | 2 |
| #89859 | 2 |
| #89803 | 2 |
| #89639 | 2 |
| #89624 | 2 |
| #89613 | 2 |
| #89605 | 2 |
| #89582 | 2 |
| #89562 | 2 |
| #3107 | 7 |