Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#6472 | C2 | semidirect |
| 3. #90217 | C2 | semidirect |
| 4. #90214 | C2 | semidirect |
| 5. C7×#424 | C2 | semidirect |
| 6. #89905 | C2 | semidirect |
| 7. C2×#6390 | C2 | semidirect |
| 8. #89621 | C2 | semidirect |
| 9. #89617 | C2 | semidirect |
| 10. #89616 | C2 | semidirect |
| 11. #89613 | C2 | semidirect |
| 96. #424 | D7 | semidirect |
| 267. C7 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6472 | 2 |
| C2×#6467 | 2 |
| #90217 | 2 |
| #90214 | 2 |
| C7×#424 | 2 |
| #89905 | 2 |
| C2×#6390 | 2 |
| #89621 | 2 |
| #89617 | 2 |
| #89616 | 2 |
| #89613 | 2 |
| #3046 | 7 |