Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1060 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 188 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×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C32×#830 | C2 | semidirect |
| 4. #11722052 | C2 | semidirect |
| 5. #11722036 | C2 | semidirect |
| 20. C2×C4⋊(C3⋊Dic3) | D3 | semidirect |
| 25. C3×#830 | D3 | semidirect |
| 81. #830 | C3⋊D3 | semidirect |
| 182. C33 | #481 | semidirect |
| 270. C32 | #4735 | semidirect |
| 271. C32 | #4968 | semidirect |
| 310. C3 | #10591125 | semidirect |
| 311. C3 | #10592434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723971 | 2 |
| C2×C3×C4⋊(C3⋊Dic3) | 2 |
| C32×#830 | 2 |
| #11722052 | 2 |
| #11722036 | 2 |
| #10592434 | 3 |
| #10591125 | 3 |