Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
724 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 106 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. C33×#99 | C2 | semidirect |
| 3. C3×#63661 | C2 | semidirect |
| 4. #10589340 | C3 | direct (N × H) |
| 9. C2×C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 12. C3×C4×C3⋊Dic3 | C4 | semidirect |
| 16. C32×#99 | D3 | semidirect |
| 17. C32×#99 | C2×C3 | semidirect |
| 18. #63661 | C2×C3 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | C3×C4 | semidirect |
| 46. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 65. C3×#99 | C3×D3 | semidirect |
| 66. C3×#99 | C3⋊D3 | semidirect |
| 150. #99 | C3×C3⋊D3 | semidirect |
| 151. C33 | #353 | semidirect |
| 232. C32 | #4474 | semidirect |
| 233. C32 | C3×#353 | semidirect |
| 272. C3 | C3×#4474 | semidirect |
| 273. C3 | #10589340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64149 | 2 |
| C33×#99 | 2 |
| C3×#63661 | 2 |
| #10589340 | 3 |
| C3×#4474 | 3 |