Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66961 | C2 | semidirect |
| 2. #10623008 | C2 | semidirect |
| 3. C2×C4×D44 | C2 | semidirect |
| 4. C11×#423 | C2 | semidirect |
| 5. #10622746 | C2 | semidirect |
| 6. #10622457 | C2 | semidirect |
| 7. #10622456 | C2 | semidirect |
| 8. #10622454 | C2 | semidirect |
| 21. #66928 | C22 | semidirect |
| 22. #66927 | C22 | semidirect |
| 29. #66922 | C22 | semidirect |
| 30. C11×C4⋊C8 | C22 | semidirect |
| 31. C11×C4⋊C8 | C22 | semidirect |
| 32. #66885 | C22 | semidirect |
| 33. #66880 | C22 | semidirect |
| 46. C2×D44 | D4 | semidirect |
| 110. #423 | D11 | semidirect |
| 127. C4×C11 | AGL(1,ℤ/8) | semidirect |
| 153. C4⋊C8 | C2×D11 | semidirect |
| 154. C4⋊C8 | C2×D11 | semidirect |
| 199. C11 | #3036 | semidirect |
| 250. C4 | #66961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66961 | 2 |
| #10623008 | 2 |
| C2×C4×D44 | 2 |
| C11×#423 | 2 |
| #10622746 | 2 |
| #10622457 | 2 |
| #10622456 | 2 |
| #10622454 | 2 |
| #3036 | 11 |