Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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. #89607 | C2 | semidirect |
| 3. #89605 | C2 | semidirect |
| 4. C7×#331 | C2 | semidirect |
| 5. #89339 | C2 | semidirect |
| 6. #89281 | C2 | semidirect |
| 7. #89277 | C2 | semidirect |
| 55. #331 | D7 | semidirect |
| 171. C7 | #1553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90407 | 2 |
| #89607 | 2 |
| #89605 | 2 |
| C7×#331 | 2 |
| #89339 | 2 |
| #89281 | 2 |
| #89277 | 2 |
| #1553 | 7 |