Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1988 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 411 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 |
|---|---|---|
| 1. C2×C33×SD16 | C2 | semidirect |
| 2. #11723985 | C2 | semidirect |
| 3. C2×#88862 | C2 | semidirect |
| 5. C2×#88861 | C2 | semidirect |
| 6. C2×#88851 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 22. C2×C32×SD16 | D3 | semidirect |
| 44. C33×C8 | D4 | semidirect |
| 45. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 69. C3⋊(C3⋊Dic3) | SD16 | semidirect |
| 70. C2×C3×SD16 | C3⋊D3 | semidirect |
| 92. C32×C8 | #67 | semidirect |
| 125. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 129. C33 | #492 | semidirect |
| 145. C3×C8 | #638 | semidirect |
| 174. C32 | #5175 | semidirect |
| 191. C8 | #6312 | semidirect |
| 206. C3 | #10592874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| #11723985 | 2 |
| C2×#88862 | 2 |
| #11723981 | 2 |
| C2×#88861 | 2 |
| C2×#88851 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #10592874 | 3 |