Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
960 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 271 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. C3×C9×C4⋊Q8 | C2 | semidirect |
| 3. Q8×C3⋊Dic9 | C2 | semidirect |
| 5. #11721745 | C2 | semidirect |
| 7. #11721707 | C2 | semidirect |
| 30. C9×C4⋊Q8 | D3 | semidirect |
| 83. C3×C4⋊Q8 | D9 | semidirect |
| 163. C4⋊Q8 | C3⋊D9 | semidirect |
| 170. C3×C9 | #541 | semidirect |
| 227. C9 | #5731 | semidirect |
| 252. C3 | #10589833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C4⋊Q8 | 2 |
| #11721856 | 2 |
| Q8×C3⋊Dic9 | 2 |
| #11721754 | 2 |
| #11721745 | 2 |
| #11721709 | 2 |
| #11721707 | 2 |
| #10596202 | 3 |
| #10589833 | 3 |