Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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×C3×Dic36 | C2 | semidirect |
| 3. #11720910 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 7. #11720268 | C2 | semidirect |
| 32. C2×Dic36 | D3 | semidirect |
| 213. C3×C9 | #464 | semidirect |
| 302. C9 | #5185 | semidirect |
| 341. C3 | #10588447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic36 | 2 |
| #11720967 | 2 |
| #11720910 | 2 |
| C2×#88423 | 2 |
| #11720537 | 2 |
| C9×#821 | 2 |
| #11720268 | 2 |
| #10590797 | 3 |
| #10588447 | 3 |