Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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. D7×C4⋊C8 | C2 | semidirect |
| 4. C7×#333 | C2 | semidirect |
| 5. #89341 | C2 | semidirect |
| 6. #89280 | C2 | semidirect |
| 7. #89280 | C2 | semidirect |
| 53. #333 | D7 | semidirect |
| 169. C7 | #1551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90416 | 2 |
| #89607 | 2 |
| D7×C4⋊C8 | 2 |
| C7×#333 | 2 |
| #89341 | 2 |
| #89280 | 2 |
| #1551 | 7 |