Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
988 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 3. C3×#63645 | C2 | semidirect |
| 4. C32×#818 | C2 | semidirect |
| 5. #11722053 | C2 | semidirect |
| 11. C8×C3⋊(C3⋊D3) | C4 | semidirect |
| 22. #63645 | D3 | semidirect |
| 25. C3×#818 | D3 | semidirect |
| 75. #818 | C3⋊D3 | semidirect |
| 158. C33 | #427 | semidirect |
| 230. C32 | #4880 | semidirect |
| 231. C32 | #4880 | semidirect |
| 263. C3 | #10590714 | semidirect |
| 264. C3 | #10592579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723413 | 2 |
| C3×#63645 | 2 |
| C32×#818 | 2 |
| #11722053 | 2 |
| #10592579 | 3 |
| #10590714 | 3 |