Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1652 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 635 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 |
|---|---|---|
| 4. #11722178 | C2 | semidirect |
| 5. #11722177 | C2 | semidirect |
| 15. #88855 | C4 | semidirect |
| 31. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 98. C33 | #428 | semidirect |
| 133. C32 | #4995 | semidirect |
| 158. C3 | #10592694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#117 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88855 | 2 |
| #11722178 | 2 |
| #11722177 | 2 |
| #10592694 | 3 |