Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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. Dic3×Dic18 | C2 | semidirect |
| 4. #11720526 | C2 | semidirect |
| 5. C3×#63368 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 21. #88423 | C4 | semidirect |
| 33. #63368 | D3 | semidirect |
| 48. C3×Dic18 | C2×C4 | semidirect |
| 49. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 89. C9×Dic3 | SD16 | semidirect |
| 134. Dic18 | C4×D3 | semidirect |
| 204. C3×C9 | C4×SD16 | semidirect |
| 286. Dic3 | #3672 | semidirect |
| 289. C9 | #4788 | semidirect |
| 327. C3 | C4×#3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#893 | 2 |
| Dic3×Dic18 | 2 |
| C2×#88423 | 2 |
| #11720526 | 2 |
| C3×#63368 | 2 |
| #11720295 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590475 | 3 |
| C4×#3672 | 3 |