Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 142 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. #11723942 | C2 | semidirect |
| 2. C2×C3×#3745 | C2 | semidirect |
| 3. #11723370 | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722026 | C2 | semidirect |
| 20. C2×#3745 | D3 | semidirect |
| 28. C3×#819 | D3 | semidirect |
| 88. #819 | C3⋊D3 | semidirect |
| 177. C33 | #472 | semidirect |
| 252. C32 | #4897 | semidirect |
| 253. C32 | #5160 | semidirect |
| 285. C3 | #10590929 | semidirect |
| 286. C3 | #10592596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723942 | 2 |
| C2×C3×#3745 | 2 |
| #11723370 | 2 |
| C32×#819 | 2 |
| #11722026 | 2 |
| #10592596 | 3 |
| #10590929 | 3 |