Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. C7×#556 | C2 | semidirect |
| 3. #89865 | C2 | semidirect |
| 4. #89859 | C2 | semidirect |
| 5. #89823 | C2 | semidirect |
| 6. #89819 | C2 | semidirect |
| 7. #89803 | C2 | semidirect |
| 8. C4×#1143 | C2 | semidirect |
| 9. D4×C7⋊C8 | C2 | semidirect |
| 10. #89774 | C2 | semidirect |
| 11. #89768 | C2 | semidirect |
| 77. #556 | D7 | 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×#556 | 2 |
| #90242 | 2 |
| #89865 | 2 |
| #89859 | 2 |
| #89823 | 2 |
| #89819 | 2 |
| #89803 | 2 |
| C4×#1143 | 2 |
| D4×C7⋊C8 | 2 |
| #89774 | 2 |
| #89768 | 2 |
| #3302 | 7 |