Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C7×#536 | C2 | semidirect |
| 3. C2×#6510 | C2 | semidirect |
| 4. C2×#6411 | C2 | semidirect |
| 5. C2×#6410 | C2 | semidirect |
| 6. #89773 | C2 | semidirect |
| 7. #89327 | C2 | semidirect |
| 71. #536 | D7 | semidirect |
| 236. C7 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#536 | 2 |
| C2×#6512 | 2 |
| C2×#6510 | 2 |
| C2×#6411 | 2 |
| C2×#6410 | 2 |
| #89773 | 2 |
| #89327 | 2 |
| #2003 | 7 |