Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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×#88521 | C2 | semidirect |
| 4. C3×#63378 | C2 | semidirect |
| 5. #11720277 | C2 | semidirect |
| 26. #63378 | D3 | semidirect |
| 65. C2×D3×C9 | Q16 | semidirect |
| 162. C3×C9 | #467 | semidirect |
| 218. C2×D3 | Dic36 | semidirect |
| 234. C9 | #4887 | semidirect |
| 267. C3 | #10588788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×D3×C8×C9 | 2 |
| #11720961 | 2 |
| C3×#63378 | 2 |
| #11720277 | 2 |
| #10590852 | 3 |
| #10588788 | 3 |