Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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×#555 | C2 | semidirect |
| 2. #90246 | C2 | semidirect |
| 3. #89856 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 5. #89811 | C2 | semidirect |
| 6. #89806 | C2 | semidirect |
| 7. C4×#1141 | C2 | semidirect |
| 8. #89784 | C2 | semidirect |
| 9. #89779 | C2 | semidirect |
| 10. #89775 | C2 | semidirect |
| 11. #89767 | C2 | semidirect |
| 75. #555 | D7 | semidirect |
| 113. C7⋊C8 | #41 | semidirect |
| 229. C7 | #3354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#555 | 2 |
| #90246 | 2 |
| #89856 | 2 |
| #89851 | 2 |
| #89811 | 2 |
| #89806 | 2 |
| C4×#1141 | 2 |
| #89784 | 2 |
| #89779 | 2 |
| #89775 | 2 |
| #89767 | 2 |
| #3354 | 7 |