Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#66923 | C2 | semidirect |
| 3. C4×C11×M16 | C2 | semidirect |
| 4. #10622746 | C2 | semidirect |
| 5. #10622326 | C2 | semidirect |
| 6. #10622316 | C2 | semidirect |
| 7. #10622310 | C2 | semidirect |
| 69. C4×M16 | D11 | semidirect |
| 122. C11 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623008 | 2 |
| C2×#66923 | 2 |
| C4×C11×M16 | 2 |
| #10622746 | 2 |
| #10622326 | 2 |
| #10622316 | 2 |
| #10622310 | 2 |
| #3142 | 11 |