Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1084 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1084 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11723988 | C2 | semidirect |
| 2. C2×C3×#3756 | C2 | semidirect |
| 3. C2×C32×#215 | C2 | semidirect |
| 4. #11723434 | C2 | semidirect |
| 5. C2×#88797 | C2 | semidirect |
| 7. #11722018 | C2 | semidirect |
| 27. C2×#3756 | D3 | semidirect |
| 32. C2×C3×#215 | D3 | semidirect |
| 104. C2×#215 | C3⋊D3 | semidirect |
| 220. C33 | #495 | semidirect |
| 313. C32 | #5168 | semidirect |
| 314. C32 | #5191 | semidirect |
| 353. C3 | #10591610 | semidirect |
| 354. C3 | #10592867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723988 | 2 |
| C2×C3×#3756 | 2 |
| C2×C32×#215 | 2 |
| #11723434 | 2 |
| C2×#88797 | 2 |
| C2×#88790 | 2 |
| #11722018 | 2 |
| #10592867 | 3 |
| #10591610 | 3 |