Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×#88524 | C2 | semidirect |
| 3. #11720913 | C2 | semidirect |
| 4. C2×#88424 | C2 | semidirect |
| 5. C9×#821 | C2 | semidirect |
| 6. C3×Dic9⋊C8 | C2 | semidirect |
| 7. #11720267 | C2 | semidirect |
| 36. Dic9⋊C8 | D3 | semidirect |
| 45. #6226 | D4 | semidirect |
| 99. C3×Dic9 | SD16 | semidirect |
| 112. #821 | D9 | semidirect |
| 225. Dic9 | #204 | semidirect |
| 233. C3×C9 | #460 | semidirect |
| 338. C9 | #4848 | semidirect |
| 384. C3 | #10588442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11721040 | 2 |
| #11720913 | 2 |
| C2×#88424 | 2 |
| C9×#821 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720267 | 2 |
| #10590879 | 3 |
| #10588442 | 3 |