Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 635 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×C33×M16 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 4. #11722191 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 11. #89076 | C4 | semidirect |
| 20. C2×C32×M16 | D3 | semidirect |
| 35. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 38. #6308 | C2×C4 | semidirect |
| 66. C2×C3×M16 | C3⋊D3 | semidirect |
| 117. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 121. C33 | #417 | semidirect |
| 167. C32 | #5133 | semidirect |
| 201. C3 | #10592832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×M16 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11722191 | 2 |
| #11722186 | 2 |
| #10592832 | 3 |