Finite Group DatabasebetaFinite Group DatabasebetaOrder 1584.
152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×C11×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C3×C11×Dic3 | C2 | semidirect |
| 9. C2×C3×D3×C11 | C4 | semidirect |
| 18. C2×C11×Dic3 | D3 | semidirect |
| 24. (C2×D3)⋊Dic3 | C11 | direct (N × H) |
| 33. C2×D3×C11 | Dic3 | semidirect |
| 39. C32×C11 | C22⋊C4 | semidirect |
| 44. C2×C3⋊Dic3 | C2×C11 | semidirect |
| 45. C2×C3×Dic3 | C2×C11 | semidirect |
| 68. C2×C3×D3 | C4×C11 | semidirect |
| 72. C3×C11 | (C2×D3)⋊C4 | semidirect |
| 73. C3×C11 | #217 | semidirect |
| 80. C2×Dic3 | D3×C11 | semidirect |
| 98. C2×D3 | C11×Dic3 | semidirect |
| 104. C11 | (C2×D3)⋊Dic3 | direct (N × H) |
| 105. C32 | C11×C22⋊C4 | semidirect |
| 127. C3 | C11×(C2×D3)⋊C4 | semidirect |
| 128. C3 | C11×#217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D3×C11 | 2 |
| C2×C11×C3⋊Dic3 | 2 |
| C2×C3×C11×Dic3 | 2 |
| C11×#217 | 3 |
| C11×(C2×D3)⋊C4 | 3 |
| (C2×D3)⋊Dic3 | 11 |