Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 623 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 623 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 |
|---|---|---|
| 8. C33×M16 | C4 | semidirect |
| 11. C4⋊(C3⋊(C3⋊Dic3)) | C4 | semidirect |
| 14. C4×C3⋊(C3⋊Dic3) | C4 | semidirect |
| 33. C32×M16 | Dic3 | semidirect |
| 72. C3×M16 | C3⋊Dic3 | semidirect |
| 92. C33 | #339 | semidirect |
| 111. M16 | C3⋊(C3⋊Dic3) | semidirect |
| 128. C32 | #4555 | semidirect |
| 154. C3 | #10589421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #10589421 | 3 |