Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
864 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11723992 | C2 | semidirect |
| 3. C32×#948 | C2 | semidirect |
| 4. C2×#88796 | C2 | semidirect |
| 5. #11722058 | C2 | semidirect |
| 6. #11722030 | C2 | semidirect |
| 7. #11722026 | C2 | semidirect |
| 32. C3×#948 | D3 | semidirect |
| 107. #948 | C3⋊D3 | semidirect |
| 226. C33 | #471 | semidirect |
| 317. C32 | #5141 | semidirect |
| 318. C32 | #5200 | semidirect |
| 355. C3 | #10591679 | semidirect |
| 356. C3 | #10592840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723992 | 2 |
| C3×#64158 | 2 |
| C32×#948 | 2 |
| C2×#88796 | 2 |
| #11722058 | 2 |
| #11722030 | 2 |
| #11722026 | 2 |
| #10592840 | 3 |
| #10591679 | 3 |