Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #90261 | C2 | semidirect |
| 3. C7×#462 | C2 | semidirect |
| 5. Q16×Dic7 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 11. #89568 | C2 | semidirect |
| 81. #462 | D7 | semidirect |
| 211. C7 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90423 | 2 |
| #90261 | 2 |
| C7×#462 | 2 |
| #89957 | 2 |
| Q16×Dic7 | 2 |
| #89853 | 2 |
| C4×#1143 | 2 |
| #89618 | 2 |
| #89602 | 2 |
| #89572 | 2 |
| #89568 | 2 |
| #3364 | 7 |