Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 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. #90209 | C2 | semidirect |
| 4. #89791 | C2 | semidirect |
| 5. #89790 | C2 | semidirect |
| 6. C4×#1142 | C2 | semidirect |
| 7. #89781 | C2 | semidirect |
| 8. #89772 | C2 | semidirect |
| 9. #89768 | C2 | semidirect |
| 22. #6433 | C22 | semidirect |
| 23. #6432 | C22 | semidirect |
| 24. C4×Dic14 | C22 | semidirect |
| 28. #6384 | C22 | semidirect |
| 29. #6384 | C22 | semidirect |
| 30. #6382 | C22 | semidirect |
| 31. #6381 | C22 | semidirect |
| 32. C4⋊(C7⋊C8) | C22 | semidirect |
| 33. #6377 | C22 | semidirect |
| 34. C4×C7⋊C8 | C22 | semidirect |
| 186. C7 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#518 | 2 |
| #90209 | 2 |
| #89990 | 2 |
| #89791 | 2 |
| #89790 | 2 |
| C4×#1142 | 2 |
| #89781 | 2 |
| #89772 | 2 |
| #89768 | 2 |
| #3123 | 7 |