Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 135 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. #11721838 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. C2×#88523 | C2 | semidirect |
| 4. #11721751 | C2 | semidirect |
| 5. C3×C9×#102 | C2 | semidirect |
| 6. #11720543 | C2 | semidirect |
| 7. #11720526 | C2 | semidirect |
| 34. C9×#102 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 105. C3×#102 | D9 | semidirect |
| 214. #102 | C3⋊D9 | semidirect |
| 215. C3×C9 | #469 | semidirect |
| 306. C9 | #4782 | semidirect |
| 351. C3 | #10588462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721838 | 2 |
| C2×#88544 | 2 |
| C2×#88523 | 2 |
| #11721751 | 2 |
| C3×C9×#102 | 2 |
| #11720543 | 2 |
| #11720526 | 2 |
| #10592481 | 3 |
| #10588462 | 3 |