Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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×#467 | C2 | semidirect |
| 3. #89960 | C2 | semidirect |
| 4. Q16×Dic7 | C2 | semidirect |
| 6. C2×#6392 | C2 | semidirect |
| 7. #89815 | C2 | semidirect |
| 8. #89652 | C2 | semidirect |
| 9. #89650 | C2 | semidirect |
| 10. #89586 | C2 | semidirect |
| 11. #89568 | C2 | semidirect |
| 76. #467 | D7 | semidirect |
| 206. C7 | #3336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90333 | 2 |
| C7×#467 | 2 |
| #89960 | 2 |
| Q16×Dic7 | 2 |
| C8×C22⋊D7 | 2 |
| C2×#6392 | 2 |
| #89815 | 2 |
| #89652 | 2 |
| #89650 | 2 |
| #89586 | 2 |
| #89568 | 2 |
| #3336 | 7 |