Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. C11×#467 | C2 | semidirect |
| 3. C2×#66892 | C2 | semidirect |
| 4. C22⋊(C11⋊C16) | C2 | semidirect |
| 5. #10622129 | C2 | semidirect |
| 7. C2×C11×Q16 | C22 | semidirect |
| 13. C11×#107 | C22 | semidirect |
| 16. C2×C11⋊C16 | C22 | semidirect |
| 56. #467 | D11 | semidirect |
| 61. C22×C11 | SD32 | semidirect |
| 73. C2×Q16 | C2×D11 | semidirect |
| 81. #107 | C2×D11 | semidirect |
| 106. C11 | #2187 | semidirect |
| 131. C22 | #66892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D88 | 2 |
| C11×#467 | 2 |
| C2×#66892 | 2 |
| C22⋊(C11⋊C16) | 2 |
| #10622129 | 2 |
| #2187 | 11 |