Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C3⋊#63421 | C2 | semidirect |
| 5. C3×#41⋊C9 | C4 | semidirect |
| 30. #41⋊C9 | Dic3 | semidirect |
| 65. C3×#41 | Dic9 | semidirect |
| 127. #41 | C3⋊Dic9 | semidirect |
| 176. C3 | #10589526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3⋊#63421 | 2 |
| #10592932 | 3 |
| #10589526 | 3 |
| C4×C3⋊Dic9 | 4 |