Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3052 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3052 conjugacy classes of subgroups — too many to draw. Only its 667 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. C33×C22⋊Q8 | C2 | semidirect |
| 2. #11723987 | C2 | semidirect |
| 4. C2×#88857 | C2 | semidirect |
| 5. #11723939 | C2 | semidirect |
| 6. #11723935 | C2 | semidirect |
| 7. #11723931 | C2 | semidirect |
| 8. #11723927 | C2 | semidirect |
| 9. #11723922 | C2 | semidirect |
| 32. C32×C22⋊Q8 | D3 | semidirect |
| 93. C3×C22⋊Q8 | C3⋊D3 | semidirect |
| 164. C22⋊Q8 | C3⋊(C3⋊D3) | semidirect |
| 168. C33 | #539 | semidirect |
| 225. C32 | #5645 | semidirect |
| 261. C3 | #10596116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊Q8 | 2 |
| #11723987 | 2 |
| #11723971 | 2 |
| C2×#88857 | 2 |
| #11723939 | 2 |
| #11723935 | 2 |
| #11723931 | 2 |
| #11723927 | 2 |
| #11723922 | 2 |
| #10596116 | 3 |