Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. C7×#559 | C2 | semidirect |
| 2. #90270 | C2 | semidirect |
| 4. #89842 | C2 | semidirect |
| 5. #89829 | C2 | semidirect |
| 6. #89828 | C2 | semidirect |
| 7. C4×#1143 | C2 | semidirect |
| 8. Q8×C7⋊C8 | C2 | semidirect |
| 9. #89793 | C2 | semidirect |
| 10. C4×#1141 | C2 | semidirect |
| 11. #89781 | C2 | semidirect |
| 74. #559 | D7 | semidirect |
| 222. C7 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#559 | 2 |
| #90270 | 2 |
| #89844 | 2 |
| #89842 | 2 |
| #89829 | 2 |
| #89828 | 2 |
| C4×#1143 | 2 |
| Q8×C7⋊C8 | 2 |
| #89793 | 2 |
| C4×#1141 | 2 |
| #89781 | 2 |
| #3361 | 7 |