Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. #90161 | C2 | semidirect |
| 3. C7×#431 | C2 | semidirect |
| 4. #89614 | C2 | semidirect |
| 5. #89613 | C2 | semidirect |
| 7. #89493 | C2 | semidirect |
| 8. C4×#1132 | C2 | semidirect |
| 23. #6432 | C22 | semidirect |
| 24. #6432 | C22 | semidirect |
| 26. C4×Dic14 | C22 | semidirect |
| 27. C7×C4⋊C8 | C22 | semidirect |
| 29. C4×C7×C8 | C22 | semidirect |
| 31. #6391 | C22 | semidirect |
| 32. #6390 | C22 | semidirect |
| 72. #431 | D7 | semidirect |
| 80. C2×C4×C7 | SD16 | semidirect |
| 118. C4⋊C8 | C2×D7 | semidirect |
| 122. C4×C8 | C2×D7 | semidirect |
| 194. C2×C4 | #1132 | semidirect |
| 202. C7 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D28 | 2 |
| #90161 | 2 |
| C7×#431 | 2 |
| #89614 | 2 |
| #89613 | 2 |
| #89503 | 2 |
| #89493 | 2 |
| C4×#1132 | 2 |
| #3101 | 7 |