Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
912 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 154 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×#88863 | C2 | semidirect |
| 3. #11723399 | C2 | semidirect |
| 5. C3×#63662 | C2 | semidirect |
| 6. Dic3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 32. #63662 | D3 | semidirect |
| 218. C33 | #464 | semidirect |
| 309. C32 | #4798 | semidirect |
| 310. C32 | #5054 | semidirect |
| 349. C3 | #10591577 | 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×#88863 | 2 |
| C32×#947 | 2 |
| #11723399 | 2 |
| C2×#88794 | 2 |
| C3×#63662 | 2 |
| Dic3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722031 | 2 |
| #10592753 | 3 |
| #10591577 | 3 |