Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
429 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 6. C4×#3746 | C3 | semidirect |
| 15. #3746⋊C3 | C4 | direct (N × H) |
| 53. #3746 | C3×C4 | semidirect |
| 60. C4×H(3,𝔽3) | Q16 | semidirect |
| 144. C32×C4 | Dic12 | semidirect |
| 145. C32×C4 | C3×Q16 | semidirect |
| 159. H(3,𝔽3) | C4×Q16 | semidirect |
| 236. C32 | C4×Dic12 | semidirect |
| 237. C32 | C3×C4×Q16 | semidirect |
| 263. C4 | #3746⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746⋊C3 | 2 |
| C4×#634⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #63645⋊C3 | 2 |
| #63643⋊C3 | 2 |
| C4×#3746 | 3 |
| C3×C4×Dic12 | 3 |