Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #10623258 | C2 | semidirect |
| 2. C11×#500 | C2 | semidirect |
| 3. #10622700 | C2 | semidirect |
| 4. #10622503 | C2 | semidirect |
| 5. #10622487 | C2 | semidirect |
| 8. C8×Dic22 | C2 | semidirect |
| 48. D88 | Q8 | semidirect |
| 60. D44 | C2×Q8 | semidirect |
| 64. Dic22 | D8 | semidirect |
| 66. C8×C11 | C2×Q8 | semidirect |
| 70. #500 | D11 | semidirect |
| 132. C11 | Q8×D8 | semidirect |
| 150. C8 | Q8×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623258 | 2 |
| C11×#500 | 2 |
| #10622700 | 2 |
| #10622503 | 2 |
| #10622487 | 2 |
| #10622485 | 2 |
| C4×D88 | 2 |
| C8×Dic22 | 2 |
| Q8×D8 | 11 |