Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #90419 | C2 | semidirect |
| 3. C7×#461 | C2 | semidirect |
| 4. #89946 | C2 | semidirect |
| 5. #89935 | C2 | semidirect |
| 6. #89855 | C2 | semidirect |
| 7. #89779 | C2 | semidirect |
| 8. #89618 | C2 | semidirect |
| 9. #89609 | C2 | semidirect |
| 10. #89584 | C2 | semidirect |
| 11. #89566 | C2 | semidirect |
| 91. #461 | D7 | semidirect |
| 257. C7 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| #90239 | 2 |
| C7×#461 | 2 |
| #89946 | 2 |
| #89935 | 2 |
| #89855 | 2 |
| #89779 | 2 |
| #89618 | 2 |
| #89609 | 2 |
| #89584 | 2 |
| #89566 | 2 |
| #3254 | 7 |