Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
448 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C3×#3674 | C2 | semidirect |
| 4. C3×#63431 | C2 | semidirect |
| 5. C3×#63362 | C2 | semidirect |
| 7. #10588737 | C3 | direct (N × H) |
| 24. C2×#3674 | C2×C3 | semidirect |
| 26. #63431 | C2×C3 | semidirect |
| 27. #63362 | C2×C3 | semidirect |
| 157. C3×C9 | #497 | semidirect |
| 224. C9 | C3×#497 | semidirect |
| 252. C3 | #10588737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C2×C3×#3674 | 2 |
| C2×C3×#3672 | 2 |
| C3×#63431 | 2 |
| C3×#63362 | 2 |
| C3×#5060 | 3 |
| #10588737 | 3 |