Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1391 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1391 conjugacy classes of subgroups — too many to draw. Only its 259 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. C2×C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C2×#88449 | C2 | semidirect |
| 5. #11721097 | C2 | direct (N × H) |
| 10. C2×C4×#272 | C4 | semidirect |
| 13. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 15. #88449 | C22 | semidirect |
| 18. C2×C4×C3⋊Dic3 | D3 | semidirect |
| 31. C4×#272 | C2×C4 | semidirect |
| 48. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 96. C2×H(3,𝔽3) | #117 | semidirect |
| 148. H(3,𝔽3) | C2×#117 | semidirect |
| 185. C2×C32 | #872 | semidirect |
| 227. C32 | C2×#872 | semidirect |
| 264. C2 | #11721097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| C2×C4×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88451 | 2 |
| C2×#88449 | 2 |
| #11721097 | 2 |
| C2×#63855 | 3 |