Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. Q8×D28 | C2 | semidirect |
| 3. C7×#477 | C2 | semidirect |
| 4. #89865 | C2 | semidirect |
| 5. C4×#1143 | C2 | semidirect |
| 6. #89660 | C2 | semidirect |
| 7. #89658 | C2 | semidirect |
| 8. #89613 | C2 | semidirect |
| 9. #89610 | C2 | semidirect |
| 10. #89578 | C2 | semidirect |
| 11. #89574 | C2 | semidirect |
| 81. #477 | D7 | semidirect |
| 230. C7 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90425 | 2 |
| Q8×D28 | 2 |
| C7×#477 | 2 |
| #89865 | 2 |
| C4×#1143 | 2 |
| #89660 | 2 |
| #89658 | 2 |
| #89613 | 2 |
| #89610 | 2 |
| #89578 | 2 |
| #89574 | 2 |
| #3329 | 7 |