Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 3. C7×#433 | C2 | semidirect |
| 4. #89619 | C2 | semidirect |
| 5. #89613 | C2 | semidirect |
| 7. #89495 | C2 | semidirect |
| 8. #89482 | C2 | semidirect |
| 9. C4×#1132 | C2 | semidirect |
| 22. #6433 | C22 | semidirect |
| 23. #6432 | C22 | semidirect |
| 24. C4×Dic14 | C22 | semidirect |
| 25. C7×C4⋊C8 | C22 | semidirect |
| 27. C7×#97 | C22 | semidirect |
| 28. C4×C7×C8 | C22 | semidirect |
| 31. #6392 | C22 | semidirect |
| 32. #6391 | C22 | semidirect |
| 33. #6390 | C22 | semidirect |
| 34. #6390 | C22 | semidirect |
| 72. #433 | D7 | semidirect |
| 111. C4⋊C8 | C2×D7 | semidirect |
| 117. #97 | C2×D7 | semidirect |
| 118. C4×C8 | C2×D7 | semidirect |
| 186. C7 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90212 | 2 |
| #90209 | 2 |
| C7×#433 | 2 |
| #89619 | 2 |
| #89613 | 2 |
| #89503 | 2 |
| #89495 | 2 |
| #89482 | 2 |
| C4×#1132 | 2 |
| #3123 | 7 |