Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
908 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 64. C3⋊(C3⋊Dic3) | Q16 | semidirect |
| 147. C33 | #494 | semidirect |
| 204. C32 | #5183 | semidirect |
| 205. C32 | #5183 | semidirect |
| 229. C3 | #10590905 | semidirect |
| 230. C3 | #10592882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C2×C32×Dic12 | 2 |
| #11723451 | 2 |
| C2×#88798 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #10592882 | 3 |
| #10590905 | 3 |