Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
398 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720971 | C2 | semidirect |
| 3. C8×C3⋊Dic9 | C2 | semidirect |
| 4. C9×#821 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 32. #63380 | D3 | semidirect |
| 101. #821 | D9 | semidirect |
| 213. C3×C9 | #486 | semidirect |
| 308. C9 | #4760 | semidirect |
| 352. C3 | #10588440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721043 | 2 |
| #11720971 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×#821 | 2 |
| C3×#63380 | 2 |
| #11720294 | 2 |
| #11720266 | 2 |
| #10590885 | 3 |
| #10588440 | 3 |