Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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×#475 | C2 | semidirect |
| 4. #89851 | C2 | semidirect |
| 5. C4×#1144 | C2 | semidirect |
| 6. #89634 | C2 | semidirect |
| 7. #89633 | C2 | semidirect |
| 8. #89622 | C2 | semidirect |
| 10. #89588 | C2 | semidirect |
| 11. #89586 | C2 | semidirect |
| 80. #475 | D7 | semidirect |
| 213. C7 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90423 | 2 |
| #90270 | 2 |
| C7×#475 | 2 |
| #89851 | 2 |
| C4×#1144 | 2 |
| #89634 | 2 |
| #89633 | 2 |
| #89622 | 2 |
| #89610 | 2 |
| #89588 | 2 |
| #89586 | 2 |
| #3356 | 7 |