Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 530 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×C4×C8×C9 | C2 | semidirect |
| 4. #11720535 | C2 | semidirect |
| 5. #11720518 | C2 | semidirect |
| 13. #88525 | C4 | semidirect |
| 14. #88524 | C4 | semidirect |
| 17. #88521 | C4 | semidirect |
| 25. C4×C8×C9 | D3 | semidirect |
| 71. C3×C4×C8 | D9 | semidirect |
| 139. C4×C8 | C3⋊D9 | semidirect |
| 140. C3×C9 | #443 | semidirect |
| 192. C9 | #4700 | semidirect |
| 216. C3 | #10588380 | 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×C4×C8×C9 | 2 |
| #11720535 | 2 |
| #11720518 | 2 |
| #10592399 | 3 |
| #10588380 | 3 |