Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#6433 | C2 | semidirect |
| 3. C7×#432 | C2 | semidirect |
| 4. #89619 | C2 | semidirect |
| 5. #89508 | C2 | semidirect |
| 6. #89507 | C2 | semidirect |
| 7. #89485 | C2 | semidirect |
| 8. #89474 | C2 | semidirect |
| 70. #432 | D7 | semidirect |
| 191. C7 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90168 | 2 |
| C2×#6433 | 2 |
| C7×#432 | 2 |
| #89619 | 2 |
| #89508 | 2 |
| #89507 | 2 |
| #89485 | 2 |
| #89474 | 2 |
| #3234 | 7 |