Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90233 | C2 | semidirect |
| 3. #90011 | C2 | semidirect |
| 4. #90005 | C2 | semidirect |
| 5. #89862 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 7. #89823 | C2 | semidirect |
| 8. #89817 | C2 | semidirect |
| 9. C4×#1142 | C2 | semidirect |
| 10. D4×C7⋊C8 | C2 | semidirect |
| 11. #89779 | C2 | semidirect |
| 228. C7 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#547 | 2 |
| #90233 | 2 |
| #90011 | 2 |
| #90005 | 2 |
| #89862 | 2 |
| #89853 | 2 |
| #89823 | 2 |
| #89817 | 2 |
| C4×#1142 | 2 |
| D4×C7⋊C8 | 2 |
| #89779 | 2 |
| #3302 | 7 |