Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×C7×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #90513 | C2 | semidirect |
| 3. C2×#6495 | C2 | semidirect |
| 4. #90436 | C2 | semidirect |
| 5. #90009 | C2 | semidirect |
| 6. C2×#6407 | C2 | semidirect |
| 7. #89949 | C2 | semidirect |
| 8. #89932 | C2 | semidirect |
| 9. #89897 | C2 | semidirect |
| 15. C2×C7×SD16 | C22 | semidirect |
| 16. C2×C7×D8 | C22 | semidirect |
| 21. #6505 | C22 | semidirect |
| 25. #6495 | C22 | semidirect |
| 32. #6464 | C22 | semidirect |
| 33. #6410 | C22 | semidirect |
| 34. #6407 | C22 | semidirect |
| 35. #6407 | C22 | semidirect |
| 36. #6393 | C22 | semidirect |
| 86. C2×AGL(1,ℤ/8) | D7 | semidirect |
| 145. C2×SD16 | C2×D7 | semidirect |
| 147. C2×D8 | C2×D7 | semidirect |
| 269. C7 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×AGL(1,ℤ/8) | 2 |
| #90513 | 2 |
| C2×#6495 | 2 |
| #90436 | 2 |
| #90009 | 2 |
| C2×#6407 | 2 |
| #89949 | 2 |
| #89932 | 2 |
| #89897 | 2 |
| #3068 | 7 |