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×#88447 | C2 | semidirect |
| 5. #11721089 | C2 | direct (N × H) |
| 10. C2×C4×#272 | C4 | semidirect |
| 13. C4⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 15. #88447 | C22 | semidirect |
| 18. C2×C4⋊(C3⋊Dic3) | D3 | semidirect |
| 31. C4×#272 | C2×C4 | semidirect |
| 48. C4⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 97. C2×H(3,𝔽3) | #117 | semidirect |
| 151. H(3,𝔽3) | C2×#117 | semidirect |
| 189. C2×C32 | #892 | semidirect |
| 234. C32 | C2×#892 | semidirect |
| 272. C2 | #11721089 | 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×#88447 | 2 |
| #11721089 | 2 |
| C2×#63841 | 3 |