Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic22 | C2 | semidirect |
| 3. C2×#66928 | C2 | semidirect |
| 4. C4×C11×C22⋊C4 | C2 | semidirect |
| 5. #10622571 | C2 | semidirect |
| 6. #10622542 | C2 | semidirect |
| 7. #10622286 | C2 | semidirect |
| 45. C2×Dic22 | D4 | semidirect |
| 85. C4×C22⋊C4 | D11 | semidirect |
| 89. C22×C11 | #124 | semidirect |
| 152. C11 | #2436 | semidirect |
| 187. C22 | #66928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic22 | 2 |
| C2×#66983 | 2 |
| C2×#66928 | 2 |
| C4×C11×C22⋊C4 | 2 |
| #10622571 | 2 |
| #10622542 | 2 |
| #10622286 | 2 |
| #2436 | 11 |