Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 7. C3×C3⋊(C3⋊C16) | C4 | semidirect |
| 30. C3⋊(C3⋊C16) | Dic3 | semidirect |
| 99. C33 | #367 | semidirect |
| 156. C32 | #4490 | semidirect |
| 157. C32 | #4505 | semidirect |
| 181. C3 | #10589141 | semidirect |
| 182. C3 | #10589142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63645 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589142 | 3 |
| #10589141 | 3 |