Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 169 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. C3×#63362 | C2 | semidirect |
| 5. Dic3×C9⋊C8 | C2 | semidirect |
| 15. #88420 | C4 | semidirect |
| 25. #63362 | D3 | semidirect |
| 34. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 35. C3×C9⋊C8 | C2×C4 | semidirect |
| 62. C9×Dic3 | M16 | semidirect |
| 94. C9⋊C8 | C4×D3 | semidirect |
| 139. C3×C9 | C4×M16 | semidirect |
| 192. Dic3 | #3667 | semidirect |
| 196. C9 | #4707 | semidirect |
| 222. C3 | C4×#3667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D3×C9 | 2 |
| C2×#88420 | 2 |
| #11720516 | 2 |
| C3×#63362 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590334 | 3 |
| C4×#3667 | 3 |