Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 50. C3×C4×C9 | Q16 | semidirect |
| 111. C4×C9 | Dic12 | semidirect |
| 119. C3×C9 | #494 | semidirect |
| 157. C3×C4 | #3674 | semidirect |
| 167. C9 | #4699 | semidirect |
| 184. C4 | #88428 | semidirect |
| 187. C3 | #10588765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C9×#869 | 2 |
| C2×#88428 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #10590386 | 3 |
| #10588765 | 3 |