Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22×C3×Dic18 | C2 | semidirect |
| 3. C2×#88416 | C2 | semidirect |
| 4. C9×#830 | C2 | semidirect |
| 5. #11720276 | C2 | semidirect |
| 22. C22×Dic18 | D3 | semidirect |
| 42. C3×Dic18 | D4 | semidirect |
| 75. C22×C3×C9 | SD16 | semidirect |
| 93. #830 | D9 | semidirect |
| 129. Dic18 | #67 | semidirect |
| 181. C22×C9 | #215 | semidirect |
| 201. C3×C9 | #448 | semidirect |
| 272. C22×C3 | #3664 | semidirect |
| 298. C9 | #5227 | semidirect |
| 333. C22 | #88416 | semidirect |
| 340. C3 | #10588404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic18 | 2 |
| #11721819 | 2 |
| C2×#88416 | 2 |
| C9×#830 | 2 |
| #11720276 | 2 |
| #10591174 | 3 |
| #10588404 | 3 |