Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 3. #11720516 | C2 | semidirect |
| 4. C9×#803 | C2 | semidirect |
| 5. C3⋊C8×Dic9 | C2 | semidirect |
| 15. #88413 | C4 | semidirect |
| 34. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 35. C9×C3⋊C8 | C2×C4 | semidirect |
| 62. C3×Dic9 | M16 | semidirect |
| 72. #803 | D9 | semidirect |
| 132. Dic9 | #208 | semidirect |
| 139. C3×C9 | C4×M16 | semidirect |
| 160. C3⋊C8 | C4×D9 | semidirect |
| 196. C9 | C4×#208 | semidirect |
| 222. C3 | #10588388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×D9 | 2 |
| C2×#88413 | 2 |
| #11720516 | 2 |
| C9×#803 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10590334 | 3 |
| #10588388 | 3 |