Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
352 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11720878 | C2 | semidirect |
| 3. #11720538 | C2 | semidirect |
| 4. C3×#63372 | C2 | semidirect |
| 5. #11720300 | C2 | semidirect |
| 13. C9×Dic12 | C4 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 15. C9×#204 | C4 | semidirect |
| 28. #63372 | D3 | semidirect |
| 128. Dic12 | Dic9 | semidirect |
| 129. D24 | Dic9 | semidirect |
| 130. #204 | Dic9 | semidirect |
| 154. C3×C9 | #444 | semidirect |
| 216. C9 | #4894 | semidirect |
| 242. 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 |
| #11720878 | 2 |
| #11720538 | 2 |
| C3×#63372 | 2 |
| #11720300 | 2 |
| #10590920 | 3 |
| #10588877 | 3 |