Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 7. C22×C3×Dic9 | C4 | semidirect |
| 10. C3×#3676 | C4 | semidirect |
| 40. C22×Dic9 | Dic3 | semidirect |
| 45. #3676 | Dic3 | semidirect |
| 135. C3×C9 | #352 | semidirect |
| 205. C9 | #4539 | semidirect |
| 237. C3 | #10588152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63497 | 2 |
| #11720577 | 2 |
| C9×#833 | 2 |
| #10589176 | 3 |
| #10588152 | 3 |