Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×D7×Q16 | C2 | semidirect |
| 4. C7×#467 | C2 | semidirect |
| 5. #89960 | C2 | semidirect |
| 6. #89888 | C2 | semidirect |
| 7. #89824 | C2 | semidirect |
| 8. #89659 | C2 | semidirect |
| 9. #89652 | C2 | semidirect |
| 10. #89588 | C2 | semidirect |
| 11. #89574 | C2 | semidirect |
| 90. #467 | D7 | semidirect |
| 249. C7 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q16 | 2 |
| C2×#6464 | 2 |
| #90319 | 2 |
| C7×#467 | 2 |
| #89960 | 2 |
| #89888 | 2 |
| #89824 | 2 |
| #89659 | 2 |
| #89652 | 2 |
| #89588 | 2 |
| #89574 | 2 |
| #3059 | 7 |