Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 153 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×#121 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721819 | C2 | semidirect |
| 4. C2×#88532 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720528 | C2 | semidirect |
| 7. #11720526 | C2 | semidirect |
| 30. C9×#121 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 97. C3×#121 | D9 | semidirect |
| 211. #121 | C3⋊D9 | semidirect |
| 215. C3×C9 | #469 | semidirect |
| 306. C9 | #5039 | semidirect |
| 351. C3 | #10588722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#121 | 2 |
| C2×#88544 | 2 |
| #11721819 | 2 |
| C2×#88532 | 2 |
| #11720576 | 2 |
| #11720528 | 2 |
| #11720526 | 2 |
| #10592738 | 3 |
| #10588722 | 3 |