Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C3×Dic36 | C2 | semidirect |
| 4. #11720930 | C2 | semidirect |
| 5. C2×#88427 | C2 | semidirect |
| 7. #11720538 | C2 | semidirect |
| 35. C2×Dic36 | D3 | semidirect |
| 207. C3×C9 | #497 | semidirect |
| 289. C9 | #5190 | semidirect |
| 324. C3 | #10588847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| C2×C3×Dic36 | 2 |
| #11720967 | 2 |
| #11720930 | 2 |
| C2×#88427 | 2 |
| C2×#88423 | 2 |
| #11720538 | 2 |
| #10590870 | 3 |
| #10588847 | 3 |