Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 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×#555 | C2 | semidirect |
| 2. #90244 | C2 | semidirect |
| 3. #89863 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. #89810 | C2 | semidirect |
| 6. #89809 | C2 | semidirect |
| 7. C4×#1142 | C2 | semidirect |
| 8. #89787 | C2 | semidirect |
| 9. D4×C7⋊C8 | C2 | semidirect |
| 10. #89775 | C2 | semidirect |
| 11. #89774 | C2 | semidirect |
| 77. #555 | D7 | semidirect |
| 239. C7 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#555 | 2 |
| #90244 | 2 |
| #89863 | 2 |
| #89860 | 2 |
| #89810 | 2 |
| #89809 | 2 |
| C4×#1142 | 2 |
| #89787 | 2 |
| D4×C7⋊C8 | 2 |
| #89775 | 2 |
| #89774 | 2 |
| #3305 | 7 |