Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×C9×Dic6 | C2 | semidirect |
| 3. C2×#88428 | C2 | semidirect |
| 5. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 37. C4⋊(C9⋊C8) | D3 | semidirect |
| 105. C4×Dic6 | D9 | semidirect |
| 225. C3×C9 | #464 | semidirect |
| 323. C9 | #4845 | semidirect |
| 363. C3 | #10588711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C4×C9×Dic6 | 2 |
| C2×#88428 | 2 |
| C2×#88426 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720269 | 2 |
| #11720267 | 2 |
| #10590368 | 3 |
| #10588711 | 3 |