Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3304 conjugacy classes of subgroups; only the 723 normal subgroups are shown.
This group has 3304 conjugacy classes of subgroups — too many to draw. Only its 723 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×C4×Q8 | C2 | semidirect |
| 2. #11723988 | C2 | semidirect |
| 3. #11723935 | C2 | semidirect |
| 4. #11723934 | C2 | semidirect |
| 5. #11723916 | C2 | semidirect |
| 7. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 8. C4×#6308 | C2 | semidirect |
| 26. C32×C4×Q8 | D3 | semidirect |
| 76. C3×C4×Q8 | C3⋊D3 | semidirect |
| 135. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 138. C33 | #559 | semidirect |
| 184. C32 | #5585 | semidirect |
| 214. C3 | #10596056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| #11723988 | 2 |
| #11723935 | 2 |
| #11723934 | 2 |
| #11723916 | 2 |
| #11723915 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C4×#6308 | 2 |
| #10596056 | 3 |