Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
356 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 123 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. C7×#477 | C2 | semidirect |
| 4. #89850 | C2 | semidirect |
| 5. C4×#1144 | C2 | semidirect |
| 6. #89656 | C2 | semidirect |
| 7. D7×#107 | C2 | semidirect |
| 8. #89622 | C2 | semidirect |
| 10. #89585 | C2 | semidirect |
| 11. #89581 | C2 | semidirect |
| 80. #477 | D7 | semidirect |
| 99. D28 | Q16 | semidirect |
| 215. C7 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90421 | 2 |
| #90270 | 2 |
| C7×#477 | 2 |
| #89850 | 2 |
| C4×#1144 | 2 |
| #89656 | 2 |
| D7×#107 | 2 |
| #89622 | 2 |
| #89606 | 2 |
| #89585 | 2 |
| #89581 | 2 |
| #3338 | 7 |