Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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×C9×Dic12 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 4. #11720243 | C2 | direct (N × H) |
| 13. C9×Dic12 | C22 | semidirect |
| 14. C3×C9⋊C16 | C22 | semidirect |
| 23. C2×C9⋊C16 | D3 | semidirect |
| 54. C9⋊C16 | C2×D3 | semidirect |
| 62. C2×Dic12 | D9 | semidirect |
| 95. C2×C3×C9 | SD32 | semidirect |
| 109. Dic12 | C2×D9 | semidirect |
| 139. C3×C9 | C2×SD32 | semidirect |
| 169. C2×C9 | #800 | semidirect |
| 200. C9 | C2×#800 | semidirect |
| 212. C2×C3 | #63387 | semidirect |
| 226. C3 | C2×#63387 | semidirect |
| 229. C2 | #11720243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C9×Dic12 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #11720243 | 2 |
| C2×#63549 | 3 |
| C2×#63387 | 3 |