Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1404 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 1404 conjugacy classes of subgroups — too many to draw. Only its 162 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. #11723981 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. C2×C32×#213 | C2 | semidirect |
| 4. #11723529 | C2 | semidirect |
| 5. C2×#88791 | C2 | semidirect |
| 6. C2×#88790 | C2 | semidirect |
| 7. #11722018 | C2 | semidirect |
| 29. C2×#3753 | D3 | semidirect |
| 32. C2×C3×#213 | D3 | semidirect |
| 54. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 55. C32×C3⋊C8 | D4 | semidirect |
| 99. C3⋊(C3⋊Dic3) | D8 | semidirect |
| 110. C2×#213 | C3⋊D3 | semidirect |
| 157. C3⋊(C3⋊C8) | #67 | semidirect |
| 159. C3×C3⋊C8 | #67 | semidirect |
| 236. C33 | #493 | semidirect |
| 281. C3⋊C8 | #638 | semidirect |
| 344. C32 | #5151 | semidirect |
| 345. C32 | #5151 | semidirect |
| 393. C3 | #10591484 | semidirect |
| 394. C3 | #10592850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723981 | 2 |
| C2×C3×#3753 | 2 |
| C2×C32×#213 | 2 |
| #11723529 | 2 |
| C2×#88791 | 2 |
| C2×#88790 | 2 |
| #11722018 | 2 |
| #10592850 | 3 |
| #10591484 | 3 |