Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 1. C2×#88521 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 4. #11720241 | C2 | direct (N × H) |
| 11. #88521 | C22 | semidirect |
| 14. C3×C9⋊C16 | C22 | semidirect |
| 23. C2×C9⋊C16 | D3 | semidirect |
| 54. C9⋊C16 | C2×D3 | semidirect |
| 95. C2×C3×C9 | SD32 | semidirect |
| 138. C3×C9 | C2×SD32 | semidirect |
| 169. C2×C9 | #800 | semidirect |
| 197. C9 | C2×#800 | semidirect |
| 210. C2×C3 | #63386 | semidirect |
| 222. C3 | C2×#63386 | semidirect |
| 225. C2 | #11720241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C9×D24 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #11720241 | 2 |
| C2×#63548 | 3 |
| C2×#63386 | 3 |