Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#67043 | C2 | semidirect |
| 2. C2×C11×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C2×#66989 | C2 | semidirect |
| 4. C2×#66985 | C2 | semidirect |
| 5. C2×#66901 | C2 | semidirect |
| 6. #10622814 | C2 | direct (N × H) |
| 7. C2×#66889 | C2 | semidirect |
| 8. C2×#66888 | C2 | semidirect |
| 14. #67043 | C22 | semidirect |
| 23. C11×AGL(1,ℤ/8) | C22 | semidirect |
| 29. #66989 | C22 | semidirect |
| 32. #66985 | C22 | semidirect |
| 36. #66901 | C22 | semidirect |
| 37. #66889 | C22 | semidirect |
| 38. #66888 | C22 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D11 | semidirect |
| 193. AGL(1,ℤ/8) | C2×D11 | semidirect |
| 211. C2×C11 | #454 | semidirect |
| 273. C11 | C2×#454 | semidirect |
| 349. C2 | #10622814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67043 | 2 |
| C2×C11×AGL(1,ℤ/8) | 2 |
| C2×#66989 | 2 |
| C2×#66985 | 2 |
| C2×#66901 | 2 |
| #10622814 | 2 |
| C2×#66889 | 2 |
| C2×#66888 | 2 |
| C2×#454 | 11 |