Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1168 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 1. C2×C33×D8 | C2 | semidirect |
| 2. C3×#64149 | C2 | semidirect |
| 3. C3×#64145 | C2 | semidirect |
| 4. C2×C3×#3754 | C2 | semidirect |
| 5. C2×C3×#3753 | C2 | semidirect |
| 6. C2×C3×#3744 | C2 | semidirect |
| 7. C3×#63642 | C2 | semidirect |
| 8. #10592853 | C3 | direct (N × H) |
| 24. C2×C32×D8 | D3 | semidirect |
| 25. C2×C32×D8 | C2×C3 | semidirect |
| 26. #64149 | C2×C3 | semidirect |
| 27. #64145 | C2×C3 | semidirect |
| 28. C2×#3754 | C2×C3 | semidirect |
| 29. C2×#3753 | C2×C3 | semidirect |
| 30. C2×#3744 | C2×C3 | semidirect |
| 36. #63642 | C2×C3 | semidirect |
| 53. C33×C8 | D4 | semidirect |
| 54. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 102. C2×C3×D8 | C3×D3 | semidirect |
| 103. C2×C3×D8 | C3⋊D3 | semidirect |
| 151. C32×C8 | #67 | semidirect |
| 152. C32×C8 | C3×D4 | semidirect |
| 153. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 223. C2×D8 | C3×C3⋊D3 | semidirect |
| 227. C33 | #496 | semidirect |
| 267. C3×C8 | C3×#67 | semidirect |
| 268. C3×C8 | #638 | semidirect |
| 327. C32 | #5154 | semidirect |
| 328. C32 | C3×#496 | semidirect |
| 345. C8 | C3×#638 | semidirect |
| 372. C3 | C3×#5154 | semidirect |
| 373. C3 | #10592853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C3×#64149 | 2 |
| C3×#64145 | 2 |
| C2×C3×#3754 | 2 |
| C2×C3×#3753 | 2 |
| C2×C3×#3744 | 2 |
| C3×#63642 | 2 |
| #10592853 | 3 |
| C3×#5154 | 3 |