Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
920 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 192 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. C3×C4×#634 | C2 | semidirect |
| 3. C2×#88792 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 5. #11722031 | C2 | semidirect |
| 20. C4×#634 | D3 | semidirect |
| 36. C3×#634 | D4 | semidirect |
| 71. C33×C4 | SD16 | semidirect |
| 105. #634 | D12 | semidirect |
| 159. C32×C4 | #214 | semidirect |
| 160. C32×C4 | #215 | semidirect |
| 174. C33 | #460 | semidirect |
| 243. C3×C4 | #3715 | semidirect |
| 244. C3×C4 | #3754 | semidirect |
| 252. C32 | #5027 | semidirect |
| 253. C32 | #5075 | semidirect |
| 285. C4 | #88792 | semidirect |
| 289. C3 | #10590364 | semidirect |
| 290. C3 | #10592774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#634 | 2 |
| C32×#874 | 2 |
| C2×#88792 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722031 | 2 |
| #10592774 | 3 |
| #10590364 | 3 |