Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 407 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. C2×#89080 | C2 | semidirect |
| 2. C2×#88862 | C2 | semidirect |
| 3. C2×#88852 | C2 | semidirect |
| 4. #11723936 | C2 | semidirect |
| 5. C33×#103 | C2 | semidirect |
| 6. #11722190 | C2 | semidirect |
| 7. #11722179 | C2 | semidirect |
| 28. C32×#103 | D3 | semidirect |
| 35. C33×Q8 | D4 | semidirect |
| 45. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 86. C3×#103 | C3⋊D3 | semidirect |
| 93. C32×Q8 | D12 | semidirect |
| 150. #103 | C3⋊(C3⋊D3) | semidirect |
| 153. C33 | #449 | semidirect |
| 158. C3×Q8 | C4⋊(C3⋊D3) | semidirect |
| 210. C32 | #4810 | semidirect |
| 215. Q8 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 252. C3 | #10592509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C2×#88862 | 2 |
| C2×#88852 | 2 |
| #11723936 | 2 |
| C33×#103 | 2 |
| #11722190 | 2 |
| #11722179 | 2 |
| #10592509 | 3 |