Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C7×#427 | C2 | semidirect |
| 3. #89888 | C2 | semidirect |
| 5. #89768 | C2 | semidirect |
| 6. #89659 | C2 | semidirect |
| 7. #89652 | C2 | semidirect |
| 8. #89646 | C2 | semidirect |
| 9. #89645 | C2 | semidirect |
| 10. #89639 | C2 | semidirect |
| 11. #89626 | C2 | semidirect |
| 80. #427 | D7 | semidirect |
| 206. C7 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90224 | 2 |
| C7×#427 | 2 |
| #89888 | 2 |
| C8×C22⋊D7 | 2 |
| #89768 | 2 |
| #89659 | 2 |
| #89652 | 2 |
| #89646 | 2 |
| #89645 | 2 |
| #89639 | 2 |
| #89626 | 2 |
| #3342 | 7 |