Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 1. #11721706 | C2 | semidirect |
| 3. C2×#88428 | C2 | semidirect |
| 5. C3×#63362 | C2 | semidirect |
| 27. #63362 | D3 | semidirect |
| 152. C3×C9 | #497 | semidirect |
| 215. C9 | #4715 | semidirect |
| 242. C3 | #10588737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C9×#875 | 2 |
| C2×#88428 | 2 |
| C2×#88424 | 2 |
| C3×#63362 | 2 |
| #10590372 | 3 |
| #10588737 | 3 |