Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11721707 | C2 | semidirect |
| 3. C3×C4×C8×C9 | C2 | semidirect |
| 5. #11720539 | C2 | semidirect |
| 22. C4×C8×C9 | D3 | semidirect |
| 60. C3×C4×C8 | D9 | semidirect |
| 118. C4×C8 | C3⋊D9 | semidirect |
| 119. C3×C9 | #488 | semidirect |
| 164. C9 | #4697 | semidirect |
| 186. C3 | #10588379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| #11721707 | 2 |
| C3×C4×C8×C9 | 2 |
| #11720543 | 2 |
| #11720539 | 2 |
| #10592396 | 3 |
| #10588379 | 3 |