Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
872 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 156 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. Dic3×#634 | C2 | semidirect |
| 4. C2×#88798 | C2 | semidirect |
| 6. Dic3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 7. #11722038 | C2 | semidirect |
| 216. C33 | #464 | semidirect |
| 308. C32 | #5054 | semidirect |
| 309. C32 | #5166 | semidirect |
| 349. C3 | #10591442 | semidirect |
| 350. C3 | #10592753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3754 | 2 |
| C32×#936 | 2 |
| Dic3×#634 | 2 |
| C2×#88798 | 2 |
| #11722202 | 2 |
| Dic3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722038 | 2 |
| #10592753 | 3 |
| #10591442 | 3 |