Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1180 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 291 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. #11721836 | C2 | semidirect |
| 3. #11721835 | C2 | semidirect |
| 4. D4×C3⋊Dic9 | C2 | semidirect |
| 5. C4×#6226 | C2 | semidirect |
| 137. C3×C9 | #559 | semidirect |
| 187. C9 | #5713 | semidirect |
| 210. C3 | #10589815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| #11721836 | 2 |
| #11721835 | 2 |
| D4×C3⋊Dic9 | 2 |
| C4×#6226 | 2 |
| #10596184 | 3 |
| #10589815 | 3 |