Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3052 conjugacy classes of subgroups; only the 1075 normal subgroups are shown.
This group has 3052 conjugacy classes of subgroups — too many to draw. Only its 1075 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. #11722201 | C2 | semidirect |
| 7. C22×C33×C4 | C4 | semidirect |
| 26. C22×C32×C4 | Dic3 | semidirect |
| 57. C22×C3×C4 | C3⋊Dic3 | semidirect |
| 72. C33 | #381 | semidirect |
| 89. C22×C4 | C3⋊(C3⋊Dic3) | semidirect |
| 100. C32 | #5211 | semidirect |
| 122. C3 | #10592910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C2×#88864 | 2 |
| #11722201 | 2 |
| #10592910 | 3 |