Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 159 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. #11721770 | C2 | semidirect |
| 3. C3×C9×#97 | C2 | semidirect |
| 4. #11720535 | C2 | semidirect |
| 5. #11720518 | C2 | semidirect |
| 13. #88525 | C4 | semidirect |
| 14. #88524 | C4 | semidirect |
| 17. #88521 | C4 | semidirect |
| 25. C9×#97 | D3 | semidirect |
| 70. C3×#97 | D9 | semidirect |
| 136. #97 | C3⋊D9 | semidirect |
| 137. C3×C9 | #444 | semidirect |
| 187. C9 | #4717 | semidirect |
| 210. C3 | #10588397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| #11721770 | 2 |
| C3×C9×#97 | 2 |
| #11720535 | 2 |
| #11720518 | 2 |
| #10592416 | 3 |
| #10588397 | 3 |