Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C3×C9×#124 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 3. C2×#88547 | C2 | semidirect |
| 5. C2×#88543 | C2 | semidirect |
| 6. #11721712 | C2 | semidirect |
| 7. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 30. C9×#124 | D3 | semidirect |
| 91. C3×#124 | D9 | semidirect |
| 193. #124 | C3⋊D9 | semidirect |
| 195. C3×C9 | #495 | semidirect |
| 270. C9 | #5059 | semidirect |
| 305. C3 | #10588740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C2×#88548 | 2 |
| C2×#88547 | 2 |
| C2×#88544 | 2 |
| C2×#88543 | 2 |
| #11721712 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10592758 | 3 |
| #10588740 | 3 |