Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
280 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #11720824 | C2 | semidirect |
| 2. C16×C3⋊D9 | C2 | semidirect |
| 3. C9×D48 | C2 | semidirect |
| 4. C3×Dic72 | C2 | semidirect |
| 5. #11720240 | C2 | semidirect |
| 23. Dic72 | D3 | semidirect |
| 64. D48 | D9 | semidirect |
| 124. C3×C9 | #508 | semidirect |
| 172. C9 | #4919 | semidirect |
| 194. C3 | #10588592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720824 | 2 |
| C16×C3⋊D9 | 2 |
| C9×D48 | 2 |
| C3×Dic72 | 2 |
| #11720240 | 2 |
| #10590244 | 3 |
| #10588592 | 3 |