Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
600 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#88428 | C2 | semidirect |
| 5. #11720269 | C2 | semidirect |
| 74. C22×C3×C9 | Q16 | semidirect |
| 174. C22×C9 | Dic12 | semidirect |
| 189. C3×C9 | #451 | semidirect |
| 256. C22×C3 | #3674 | semidirect |
| 275. C9 | #4739 | semidirect |
| 303. C22 | #88428 | semidirect |
| 311. C3 | #10588726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C9×#924 | 2 |
| C2×#88428 | 2 |
| C3×#63389 | 2 |
| #11720269 | 2 |
| #10591190 | 3 |
| #10588726 | 3 |