Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C23×C8×C11 | C2 | semidirect |
| 3. C2×#66979 | C2 | semidirect |
| 4. #10622726 | C2 | direct (N × H) |
| 5. C2×#66885 | C2 | semidirect |
| 6. C2×#66880 | C2 | semidirect |
| 11. C2×#4339 | C4 | semidirect |
| 18. C22×C8×C11 | C22 | semidirect |
| 21. #66979 | C22 | semidirect |
| 24. #66885 | C22 | semidirect |
| 25. #66880 | C22 | semidirect |
| 40. #4339 | C2×C4 | semidirect |
| 89. C23×C8 | D11 | semidirect |
| 120. C22×C8 | C2×D11 | semidirect |
| 129. C2×C11 | #416 | semidirect |
| 165. C11 | C2×#416 | semidirect |
| 212. C2 | #10622726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4339 | 2 |
| C23×C8×C11 | 2 |
| C2×#66979 | 2 |
| #10622726 | 2 |
| C2×#66885 | 2 |
| C2×#66880 | 2 |
| C2×#416 | 11 |