Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
265 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 66 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. #63644⋊C3 | C2 | semidirect |
| 3. #63639⋊C3 | C2 | semidirect |
| 4. #10589432 | C3 | semidirect |
| 7. Q16×H(3,𝔽3) | C4 | semidirect |
| 9. D8×H(3,𝔽3) | C4 | semidirect |
| 16. #63644 | C2×C3 | semidirect |
| 17. #63639 | C2×C3 | semidirect |
| 35. C32×Q16 | Dic3 | semidirect |
| 36. C32×Q16 | C3×C4 | semidirect |
| 41. C32×D8 | Dic3 | semidirect |
| 42. C32×D8 | C3×C4 | semidirect |
| 139. H(3,𝔽3) | #360 | semidirect |
| 181. Q16 | (C3⋊Dic3)⋊C3 | semidirect |
| 183. D8 | (C3⋊Dic3)⋊C3 | semidirect |
| 211. C32 | #4566 | semidirect |
| 212. C32 | C3×#360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#135 | 2 |
| #63644⋊C3 | 2 |
| #63639⋊C3 | 2 |
| #10589432 | 3 |
| C3×#4566 | 3 |