Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
948 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 220 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. D12×C3⋊Dic3 | C2 | semidirect |
| 3. #11722188 | C2 | semidirect |
| 4. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 5. #11722032 | C2 | semidirect |
| 14. C32×D24 | C4 | semidirect |
| 24. C8×C3⋊Dic3 | D3 | semidirect |
| 33. C32×D12 | C2×C4 | semidirect |
| 35. C33×C8 | C2×C4 | semidirect |
| 55. C3×D24 | Dic3 | semidirect |
| 65. C3×C3⋊Dic3 | D8 | semidirect |
| 93. C3×D12 | C2×Dic3 | semidirect |
| 96. C32×C8 | C4×D3 | semidirect |
| 97. C32×C8 | C2×Dic3 | semidirect |
| 122. D24 | C3⋊Dic3 | direct (N × H) |
| 142. C3⋊Dic3 | D24 | direct (N × H) |
| 150. C33 | C4×D8 | semidirect |
| 167. D12 | C2×C3⋊Dic3 | semidirect |
| 171. C3×C8 | D3×Dic3 | semidirect |
| 172. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 216. C32 | C4×D24 | semidirect |
| 217. C32 | Dic3×D8 | semidirect |
| 227. C8 | D3×C3⋊Dic3 | semidirect |
| 249. C3 | Dic3×D24 | semidirect |
| 250. C3 | D8×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| D12×C3⋊Dic3 | 2 |
| #11722188 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #11722032 | 2 |
| D8×C3⋊Dic3 | 3 |
| Dic3×D24 | 3 |