Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2884 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 2884 conjugacy classes of subgroups — too many to draw. Only its 675 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 |
|---|---|---|
| 2. #11723985 | C2 | semidirect |
| 5. #11723930 | C2 | semidirect |
| 6. #11723930 | C2 | semidirect |
| 7. #11723929 | C2 | semidirect |
| 49. C2×C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 161. C33 | #544 | semidirect |
| 214. C32 | #5623 | semidirect |
| 246. C3 | #10596094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊Q8 | 2 |
| #11723985 | 2 |
| #11723965 | 2 |
| C2×#88857 | 2 |
| #11723930 | 2 |
| #11723929 | 2 |
| #11723919 | 2 |
| #11723918 | 2 |
| #10596094 | 3 |