Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 2. #11720877 | C2 | semidirect |
| 3. #11720535 | C2 | semidirect |
| 4. C3×#63375 | C2 | semidirect |
| 5. #11720301 | C2 | semidirect |
| 13. C9×Dic12 | C4 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 15. C9×#204 | C4 | semidirect |
| 26. #63375 | D3 | semidirect |
| 125. Dic12 | Dic9 | semidirect |
| 126. D24 | Dic9 | semidirect |
| 127. #204 | Dic9 | semidirect |
| 150. C3×C9 | #444 | semidirect |
| 210. C9 | #4717 | semidirect |
| 236. C3 | #10588877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#904 | 2 |
| #11720877 | 2 |
| #11720535 | 2 |
| C3×#63375 | 2 |
| #11720301 | 2 |
| #10590916 | 3 |
| #10588877 | 3 |