Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11720960 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C2×#88420 | C2 | semidirect |
| 5. #11720525 | C2 | semidirect |
| 6. C3×#63368 | C2 | semidirect |
| 7. #11720295 | C2 | semidirect |
| 35. #63368 | D3 | semidirect |
| 52. C3⋊(C9⋊C8) | D4 | semidirect |
| 222. C3×C9 | #468 | semidirect |
| 318. C9 | #4812 | semidirect |
| 362. C3 | #10588718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#895 | 2 |
| #11720960 | 2 |
| C2×#88423 | 2 |
| C2×#88420 | 2 |
| #11720525 | 2 |
| C3×#63368 | 2 |
| #11720295 | 2 |
| #10590515 | 3 |
| #10588718 | 3 |