Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1052 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1052 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. C2×#88862 | C2 | semidirect |
| 2. C2×C3×#3756 | C2 | semidirect |
| 3. C32×#947 | C2 | semidirect |
| 4. #11723441 | C2 | semidirect |
| 5. C2×#88792 | C2 | semidirect |
| 7. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. C2×#3756 | D3 | semidirect |
| 31. C3×#947 | D3 | semidirect |
| 99. #947 | C3⋊D3 | semidirect |
| 219. C33 | #495 | semidirect |
| 311. C32 | #5059 | semidirect |
| 312. C32 | #5191 | semidirect |
| 351. C3 | #10591609 | semidirect |
| 352. C3 | #10592758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88862 | 2 |
| C2×C3×#3756 | 2 |
| C32×#947 | 2 |
| #11723441 | 2 |
| C2×#88792 | 2 |
| C2×#88790 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| #10592758 | 3 |
| #10591609 | 3 |