Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#4314 | C2 | semidirect |
| 3. C2×#66928 | C2 | semidirect |
| 4. C2×C4×D44 | C2 | semidirect |
| 5. C2×C11×C4⋊C8 | C2 | semidirect |
| 6. C2×#66885 | C2 | semidirect |
| 7. C2×#66880 | C2 | semidirect |
| 8. #10622457 | C2 | direct (N × H) |
| 23. C2×#4314 | C22 | semidirect |
| 25. #66928 | C22 | semidirect |
| 27. C4×D44 | C22 | semidirect |
| 28. C11×C4⋊C8 | C22 | semidirect |
| 29. #66885 | C22 | semidirect |
| 30. #66880 | C22 | semidirect |
| 104. C2×C4⋊C8 | D11 | semidirect |
| 145. C4⋊C8 | C2×D11 | semidirect |
| 148. C2×C11 | #463 | semidirect |
| 188. C11 | C2×#463 | semidirect |
| 243. C2 | #10622457 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D88 | 2 |
| C22×#4314 | 2 |
| C2×#66928 | 2 |
| C2×C4×D44 | 2 |
| C2×C11×C4⋊C8 | 2 |
| C2×#66885 | 2 |
| C2×#66880 | 2 |
| #10622457 | 2 |
| C2×#463 | 11 |