Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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. C11×#518 | C2 | semidirect |
| 2. C2×#66985 | C2 | semidirect |
| 3. C22×#4323 | C2 | semidirect |
| 4. #10623056 | C2 | semidirect |
| 5. #10622629 | C2 | semidirect |
| 6. #10622628 | C2 | semidirect |
| 7. #10622615 | C2 | semidirect |
| 8. #10622614 | C2 | semidirect |
| 9. #10622612 | C2 | semidirect |
| 14. C4×D4×C11 | C22 | semidirect |
| 18. C2×#4324 | C22 | semidirect |
| 22. C2×#4323 | C22 | semidirect |
| 27. #66928 | C22 | semidirect |
| 28. #66927 | C22 | semidirect |
| 29. #66874 | C22 | semidirect |
| 30. #66873 | C22 | semidirect |
| 31. #66873 | C22 | semidirect |
| 32. C4⋊(C11⋊C8) | C22 | semidirect |
| 37. C2×D4×C11 | D4 | semidirect |
| 102. #518 | D11 | semidirect |
| 140. C4×D4 | C2×D11 | semidirect |
| 168. C2×D4 | D44 | semidirect |
| 188. C11 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#518 | 2 |
| C2×#66985 | 2 |
| C22×#4323 | 2 |
| #10623056 | 2 |
| #10622629 | 2 |
| #10622628 | 2 |
| #10622615 | 2 |
| #10622614 | 2 |
| #10622612 | 2 |
| #3041 | 11 |