Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 1680 conjugacy classes of subgroups — too many to draw. Only its 461 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. #11723910 | C2 | semidirect |
| 4. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 20. C32×C4⋊C8 | D3 | semidirect |
| 50. C33×C4 | SD16 | semidirect |
| 58. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 92. C32×C4 | #204 | semidirect |
| 100. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 102. C33 | #461 | semidirect |
| 134. C3×C4 | #3744 | semidirect |
| 139. C32 | #4841 | semidirect |
| 163. C4 | #88851 | semidirect |
| 166. C3 | #10592540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88851 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723910 | 2 |
| C33×C4⋊C8 | 2 |
| #11722186 | 2 |
| #10592540 | 3 |