Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1420 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1420 conjugacy classes of subgroups — too many to draw. Only its 390 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×C32×C4⋊Dic3 | C2 | semidirect |
| 3. C33×#95 | C2 | semidirect |
| 5. C3×#4677 | C3 | direct (N × H) |
| 14. C2×C3×C4⋊Dic3 | C2×C3 | semidirect |
| 16. C32×#95 | D3 | semidirect |
| 17. C32×#95 | C2×C3 | semidirect |
| 27. #4677 | C32 | direct (N × H) |
| 50. C2×C4⋊Dic3 | C2×C32 | semidirect |
| 52. C3×#95 | C3×D3 | semidirect |
| 53. C3×#95 | C2×C32 | semidirect |
| 111. #95 | C32×D3 | semidirect |
| 112. C33 | #399 | semidirect |
| 169. C32 | #4677 | direct (N × H) |
| 170. C32 | C3×#399 | semidirect |
| 199. C3 | C3×#4677 | direct (N × H) |
| 200. C3 | C32×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×(C2×D3)⋊C4 | 2 |
| C2×C32×C4⋊Dic3 | 2 |
| C33×#95 | 2 |
| C32×#399 | 3 |
| C3×#4677 | 3 |