Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1180 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
| 2. #11721857 | C2 | semidirect |
| 3. #11721751 | C2 | semidirect |
| 4. #11721748 | C2 | semidirect |
| 5. C4×C4⋊(C3⋊D9) | C2 | semidirect |
| 23. C9×C4⋊Q8 | D3 | semidirect |
| 67. C3×C4⋊Q8 | D9 | semidirect |
| 135. C4⋊Q8 | C3⋊D9 | semidirect |
| 140. C3×C9 | #555 | semidirect |
| 192. C9 | #5734 | semidirect |
| 216. C3 | #10589836 | 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 |
| #11721857 | 2 |
| #11721751 | 2 |
| #11721748 | 2 |
| C4×C4⋊(C3⋊D9) | 2 |
| #10596205 | 3 |
| #10589836 | 3 |