Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
828 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 260 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. #11722187 | C2 | semidirect |
| 4. C3×#63644 | C2 | semidirect |
| 5. #11722055 | C2 | semidirect |
| 13. C32×D3×C8 | C4 | semidirect |
| 24. #63644 | D3 | semidirect |
| 53. C3×D3×C8 | Dic3 | semidirect |
| 117. D3×C8 | C3⋊Dic3 | semidirect |
| 143. C33 | #427 | semidirect |
| 202. C32 | #4860 | semidirect |
| 203. C32 | #5106 | semidirect |
| 230. C3 | #10590706 | semidirect |
| 231. C3 | #10592805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D3×C8 | 2 |
| #11723424 | 2 |
| #11722187 | 2 |
| C3×#63644 | 2 |
| #11722055 | 2 |
| #10592805 | 3 |
| #10590706 | 3 |