Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 567 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 567 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 |
|---|---|---|
| 8. C2×C33×C8 | C4 | semidirect |
| 13. #88855 | C4 | semidirect |
| 32. C2×C32×C8 | Dic3 | semidirect |
| 69. C2×C3×C8 | C3⋊Dic3 | semidirect |
| 88. C33 | #344 | semidirect |
| 109. C2×C8 | C3⋊(C3⋊Dic3) | semidirect |
| 122. C32 | #4556 | semidirect |
| 146. C3 | #10589422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| C2×#88855 | 2 |
| #10589422 | 3 |