Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11720970 | C2 | semidirect |
| 3. #11720543 | C2 | semidirect |
| 4. C3×#63380 | C2 | semidirect |
| 5. C8×C9×Dic3 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. #11720283 | C2 | semidirect |
| 35. #63380 | D3 | semidirect |
| 105. C8×Dic3 | D9 | semidirect |
| 216. C3×C9 | #486 | semidirect |
| 315. C9 | #4760 | semidirect |
| 360. C3 | #10588376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721006 | 2 |
| #11720970 | 2 |
| #11720543 | 2 |
| C3×#63380 | 2 |
| C8×C9×Dic3 | 2 |
| #11720284 | 2 |
| #11720283 | 2 |
| #10590878 | 3 |
| #10588376 | 3 |