Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
900 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 2. #11723399 | C2 | semidirect |
| 4. #11722180 | C2 | semidirect |
| 5. C3×#63635 | C2 | semidirect |
| 7. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 21. #88794 | C4 | semidirect |
| 32. #63635 | D3 | semidirect |
| 42. #6308 | C2×C4 | semidirect |
| 50. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 90. C32×Dic3 | SD16 | semidirect |
| 138. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 198. C3×Dic3 | #214 | semidirect |
| 206. C33 | C4×SD16 | semidirect |
| 290. Dic3 | #3754 | semidirect |
| 292. C32 | #4852 | semidirect |
| 293. C32 | C4×#214 | semidirect |
| 331. C3 | #10590479 | semidirect |
| 332. C3 | C4×#3754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#893 | 2 |
| #11723399 | 2 |
| C2×#88794 | 2 |
| #11722180 | 2 |
| C3×#63635 | 2 |
| #11722031 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| C4×#3754 | 3 |
| #10590479 | 3 |