Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11720913 | C2 | semidirect |
| 4. #11720539 | C2 | semidirect |
| 6. C3×#63375 | C2 | semidirect |
| 7. #11720262 | C2 | semidirect |
| 21. #88424 | C4 | semidirect |
| 35. #63375 | D3 | semidirect |
| 42. #6226 | C2×C4 | semidirect |
| 50. C3×C9⋊C8 | C2×C4 | semidirect |
| 139. C9⋊C8 | C4×D3 | semidirect |
| 206. C3×C9 | #440 | semidirect |
| 293. C9 | #4710 | semidirect |
| 331. C3 | #10588437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12×Dic9 | 2 |
| #11720913 | 2 |
| C2×#88424 | 2 |
| #11720539 | 2 |
| C9×#821 | 2 |
| C3×#63375 | 2 |
| #11720262 | 2 |
| #10590747 | 3 |
| #10588437 | 3 |