Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
524 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×C9×Dic6 | C2 | semidirect |
| 3. C2×#88425 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 42. C9×Dic6 | D4 | semidirect |
| 72. C22×C3×C9 | SD16 | semidirect |
| 82. C22×Dic6 | D9 | semidirect |
| 172. C22×C9 | #214 | semidirect |
| 188. C3×C9 | #448 | semidirect |
| 218. Dic6 | #611 | semidirect |
| 258. C22×C3 | #3675 | semidirect |
| 277. C9 | #5040 | semidirect |
| 311. C22 | #88425 | semidirect |
| 318. C3 | #10588908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic6 | 2 |
| C3×#63492 | 2 |
| C2×#88425 | 2 |
| #11720571 | 2 |
| #11720297 | 2 |
| #10591171 | 3 |
| #10588908 | 3 |