Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1140 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 228 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. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C32×C4×C3⋊C8 | C2 | semidirect |
| 4. #11722050 | C2 | semidirect |
| 23. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 25. C3×C4×C3⋊C8 | D3 | semidirect |
| 37. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 87. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 187. C33 | #431 | semidirect |
| 274. C32 | #4685 | semidirect |
| 275. C32 | #4685 | semidirect |
| 311. C3 | #10590297 | semidirect |
| 312. C3 | #10592384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊(C3⋊D3) | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C32×C4×C3⋊C8 | 2 |
| #11722050 | 2 |
| #11722024 | 2 |
| #10592384 | 3 |
| #10590297 | 3 |