Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
648 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. C4×C3⋊#622 | C2 | semidirect |
| 4. C3×C4×#622 | C2 | semidirect |
| 5. Dic3×#622 | C2 | semidirect |
| 12. #88924 | C4 | direct (N × H) |
| 22. C4×#622 | D3 | semidirect |
| 26. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 31. #6289 | C8 | semidirect |
| 33. C3⋊#622 | C2×C4 | semidirect |
| 34. C3×#622 | C2×C4 | semidirect |
| 58. C33×C4 | C2×C8 | semidirect |
| 59. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 60. C3×C3⋊Dic3 | C2×C8 | semidirect |
| 63. C32×Dic3 | C2×C8 | semidirect |
| 95. #622 | C4×D3 | semidirect |
| 100. C3⋊(C3⋊D3) | C4×C8 | semidirect |
| 135. C32×C4 | D3×C8 | semidirect |
| 139. C3⋊Dic3 | D3×C8 | semidirect |
| 150. C33 | C2×C4×C8 | semidirect |
| 217. C3×C4 | #3787 | semidirect |
| 223. Dic3 | #3787 | semidirect |
| 227. C32 | C4×D3×C8 | semidirect |
| 261. C4 | #88924 | direct (N × H) |
| 264. C3 | C4×#3787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88924 | 2 |
| C4×#6289 | 2 |
| C4×C3⋊#622 | 2 |
| C3×C4×#622 | 2 |
| Dic3×#622 | 2 |
| C4×#3787 | 3 |
| C4×D3×C8 | 9 |