Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 851 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. #11723967 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 8. C33×#41 | C4 | semidirect |
| 41. C32×#41 | Dic3 | semidirect |
| 88. C3×#41 | C3⋊Dic3 | semidirect |
| 114. C33 | #416 | semidirect |
| 135. #41 | C3⋊(C3⋊Dic3) | semidirect |
| 156. C32 | #5233 | semidirect |
| 186. C3 | #10592932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| #11723967 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722205 | 2 |
| #11722202 | 2 |
| #10592932 | 3 |