Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2604 conjugacy classes of subgroups; only the 875 normal subgroups are shown.
This group has 2604 conjugacy classes of subgroups — too many to draw. Only its 875 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 |
|---|---|---|
| 13. C4×C3⋊(C3⋊Dic3) | C4 | semidirect |
| 44. C33×C4 | C4⋊C4 | semidirect |
| 46. C3⋊(C3⋊Dic3) | C4⋊C4 | semidirect |
| 82. C32×C4 | Dic3⋊C4 | semidirect |
| 89. C33 | #384 | semidirect |
| 120. C3×C4 | #3750 | semidirect |
| 123. C32 | #4975 | semidirect |
| 148. C4 | #88857 | semidirect |
| 149. C3 | #10592674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88857 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #10592674 | 3 |