Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. #89471 | C2 | semidirect |
| 4. C7×#364 | C2 | semidirect |
| 5. #89312 | C2 | semidirect |
| 38. #364 | D7 | semidirect |
| 106. C7 | #2214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89681 | 2 |
| #89472 | 2 |
| #89471 | 2 |
| C7×#364 | 2 |
| #89312 | 2 |
| #2214 | 7 |