Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
348 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11720526 | C2 | semidirect |
| 4. C3×#63367 | C2 | semidirect |
| 5. #11720298 | C2 | semidirect |
| 6. #11720297 | C2 | semidirect |
| 35. #63367 | D3 | semidirect |
| 199. C3×C9 | #483 | semidirect |
| 283. C9 | #4862 | semidirect |
| 321. C3 | #10588723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#897 | 2 |
| D3×C4⋊Dic9 | 2 |
| #11720526 | 2 |
| C3×#63367 | 2 |
| #11720298 | 2 |
| #11720297 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10590439 | 3 |
| #10588723 | 3 |