Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2660 conjugacy classes of subgroups; only the 851 normal subgroups are shown.
This group has 2660 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. C2×#88855 | C2 | semidirect |
| 4. #11722202 | C2 | semidirect |
| 9. C2×C33×D4 | C4 | semidirect |
| 13. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 16. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 38. C2×C32×D4 | Dic3 | semidirect |
| 81. C2×C3×D4 | C3⋊Dic3 | semidirect |
| 103. C33 | #418 | semidirect |
| 124. C2×D4 | C3⋊(C3⋊Dic3) | semidirect |
| 142. C32 | #5215 | semidirect |
| 170. C3 | #10592914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| #11723967 | 2 |
| C2×#88855 | 2 |
| #11722202 | 2 |
| #10592914 | 3 |