Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
840 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 1. C2×#88853 | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722030 | C2 | semidirect |
| 28. C3×#819 | D3 | semidirect |
| 86. #819 | C3⋊D3 | semidirect |
| 168. C33 | #473 | semidirect |
| 235. C32 | #4896 | semidirect |
| 236. C32 | #5143 | semidirect |
| 264. C3 | #10590932 | semidirect |
| 265. C3 | #10592595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88853 | 2 |
| C3×#64110 | 2 |
| #11723388 | 2 |
| C32×#819 | 2 |
| #11722030 | 2 |
| #10592595 | 3 |
| #10590932 | 3 |