Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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×#3672 | C2 | semidirect |
| 3. #11720910 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. C9×#832 | C2 | semidirect |
| 6. #11720273 | C2 | semidirect |
| 7. #11720267 | C2 | semidirect |
| 32. C2×#3672 | D3 | semidirect |
| 52. C3×Dic18 | D4 | semidirect |
| 98. C3⋊Dic9 | SD16 | semidirect |
| 111. #832 | D9 | semidirect |
| 158. Dic18 | #67 | semidirect |
| 242. C3×C9 | #460 | semidirect |
| 355. C9 | #5163 | semidirect |
| 402. C3 | #10588442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C2×C3×#3672 | 2 |
| #11720910 | 2 |
| C2×#88416 | 2 |
| C9×#832 | 2 |
| #11720273 | 2 |
| #11720267 | 2 |
| #10591444 | 3 |
| #10588442 | 3 |