Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1084 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 198 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. C3×#64145 | C2 | semidirect |
| 3. C2×C3×#3754 | C2 | semidirect |
| 4. C2×C3×#3746 | C2 | semidirect |
| 5. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10592854 | C3 | direct (N × H) |
| 20. #64145 | C2×C3 | semidirect |
| 21. C2×#3754 | C2×C3 | semidirect |
| 22. C2×#3746 | C2×C3 | semidirect |
| 26. C8×C3⋊Dic3 | C2×C3 | semidirect |
| 153. C33 | #495 | semidirect |
| 217. C32 | #5155 | semidirect |
| 218. C32 | C3×#495 | semidirect |
| 246. C3 | C3×#5155 | semidirect |
| 247. C3 | #10592854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C3×#64145 | 2 |
| C2×C3×#3754 | 2 |
| C2×C3×#3746 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10592854 | 3 |
| C3×#5155 | 3 |