Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #90371 | C2 | semidirect |
| 2. C7×#495 | C2 | semidirect |
| 3. #89960 | C2 | semidirect |
| 4. Q16×Dic7 | C2 | semidirect |
| 5. #89943 | C2 | semidirect |
| 6. SD16×Dic7 | C2 | semidirect |
| 8. D8×Dic7 | C2 | semidirect |
| 9. #89828 | C2 | semidirect |
| 10. C4×C8×D7 | C2 | semidirect |
| 11. #89455 | C2 | semidirect |
| 74. #495 | D7 | semidirect |
| 214. C7 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90371 | 2 |
| C7×#495 | 2 |
| #89960 | 2 |
| Q16×Dic7 | 2 |
| #89943 | 2 |
| SD16×Dic7 | 2 |
| #89929 | 2 |
| D8×Dic7 | 2 |
| #89828 | 2 |
| C4×C8×D7 | 2 |
| #89455 | 2 |
| #3168 | 7 |