Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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. C22×C11×Q16 | C2 | semidirect |
| 2. #10623347 | C2 | semidirect |
| 3. C2×#66995 | C2 | semidirect |
| 5. #10622804 | C2 | semidirect |
| 6. #10622803 | C2 | semidirect |
| 7. #10622794 | C2 | semidirect |
| 8. #10622714 | C2 | semidirect |
| 84. C22×Q16 | D11 | semidirect |
| 155. C11 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×Q16 | 2 |
| #10623347 | 2 |
| C2×#66995 | 2 |
| C2×#66957 | 2 |
| #10622804 | 2 |
| #10622803 | 2 |
| #10622794 | 2 |
| #10622714 | 2 |
| #3156 | 11 |