Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
610 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 62. C3⋊Dic9 | Q16 | semidirect |
| 131. C3×C9 | #494 | semidirect |
| 178. C9 | #5183 | semidirect |
| 199. C3 | #10588863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11721854 | 2 |
| C2×#88547 | 2 |
| C2×#88521 | 2 |
| C8×C3⋊Dic9 | 2 |
| #10592882 | 3 |
| #10588863 | 3 |