Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 229 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. C33×#101 | C2 | semidirect |
| 3. #11722206 | C2 | semidirect |
| 13. C32×#101 | D3 | semidirect |
| 40. C3×#101 | C3⋊D3 | semidirect |
| 71. #101 | C3⋊(C3⋊D3) | semidirect |
| 72. C33 | #355 | semidirect |
| 99. C32 | #4477 | semidirect |
| 119. C3 | #10589343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723988 | 2 |
| C33×#101 | 2 |
| #11722206 | 2 |
| #10589343 | 3 |