Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1596 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 |
| 14. C2×C3⋊(C3⋊(C3⋊C8)) | C4 | semidirect |
| 91. C33 | #427 | semidirect |
| 122. C32 | #4998 | semidirect |
| 143. C3 | #10592697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#117 | 2 |
| #11723967 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722178 | 2 |
| #11722177 | 2 |
| #10592697 | 3 |