Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
230 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C4⋊(C11⋊C32) | C2 | semidirect |
| 4. Dic11⋊C32 | C2 | semidirect |
| 5. C11×C4⋊C32 | C2 | semidirect |
| 56. C4⋊C32 | D11 | direct (N × H) |
| 65. C4×D11 | C32 | semidirect |
| 88. C4×C11 | C2×C32 | semidirect |
| 93. Dic11 | C2×C32 | semidirect |
| 113. D11 | C4⋊C32 | direct (N × H) |
| 133. C11 | C2×C4⋊C32 | semidirect |
| 158. C4 | D11×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×C32 | 2 |
| C4×C16×D11 | 2 |
| C4⋊(C11⋊C32) | 2 |
| Dic11⋊C32 | 2 |
| C11×C4⋊C32 | 2 |
| C2×C4⋊C32 | 11 |