Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
518 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11720298 | C2 | semidirect |
| 74. C22×C3×C9 | Q16 | semidirect |
| 172. C22×C9 | Dic12 | semidirect |
| 188. C3×C9 | #451 | semidirect |
| 253. C22×C3 | #3674 | semidirect |
| 273. C9 | #4739 | semidirect |
| 301. C22 | #88428 | semidirect |
| 309. C3 | #10588907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic6 | 2 |
| #11721813 | 2 |
| C2×#88428 | 2 |
| C3×#63389 | 2 |
| #11720298 | 2 |
| #10591186 | 3 |
| #10588907 | 3 |