Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3472 conjugacy classes of subgroups; only the 835 normal subgroups are shown.
This group has 3472 conjugacy classes of subgroups — too many to draw. Only its 835 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. #11724685 | C2 | semidirect |
| 2. C33×#131 | C2 | semidirect |
| 3. #11723950 | C2 | semidirect |
| 4. C2×#88853 | C2 | semidirect |
| 5. #11723945 | C2 | semidirect |
| 19. C32×#131 | D3 | semidirect |
| 52. C3×#131 | C3⋊D3 | semidirect |
| 91. #131 | C3⋊(C3⋊D3) | semidirect |
| 92. C33 | #578 | semidirect |
| 123. C32 | #5753 | semidirect |
| 143. C3 | #10596224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724685 | 2 |
| C33×#131 | 2 |
| #11723950 | 2 |
| C2×#88853 | 2 |
| #11723945 | 2 |
| #10596224 | 3 |