Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1192 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 174 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. C3×#64361 | C2 | semidirect |
| 2. C3×#64149 | C2 | semidirect |
| 3. C3×#64117 | C2 | semidirect |
| 4. C33×#100 | C2 | semidirect |
| 5. C3×#63652 | C2 | semidirect |
| 6. #10592446 | C3 | direct (N × H) |
| 14. C2×C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C33×M16 | C22 | semidirect |
| 16. C3×C4×C3⋊Dic3 | C22 | semidirect |
| 19. #64361 | C2×C3 | semidirect |
| 21. #64149 | C2×C3 | semidirect |
| 22. #64117 | C2×C3 | semidirect |
| 26. C32×#100 | D3 | semidirect |
| 27. C32×#100 | C2×C3 | semidirect |
| 28. #63652 | C2×C3 | semidirect |
| 41. C3×C4⋊(C3⋊D3) | D4 | semidirect |
| 43. C3×#634 | D4 | semidirect |
| 55. C2×C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 63. C32×M16 | C2×D3 | semidirect |
| 64. C32×M16 | C22×C3 | semidirect |
| 65. C4×C3⋊Dic3 | C22×C3 | semidirect |
| 89. C3×#100 | C3×D3 | semidirect |
| 90. C3×#100 | C3⋊D3 | semidirect |
| 111. C4⋊(C3⋊D3) | C3×D4 | semidirect |
| 113. #634 | C3×D4 | semidirect |
| 150. C3×M16 | C2×C3×D3 | semidirect |
| 151. C3×M16 | C2×C3⋊D3 | semidirect |
| 184. #100 | C3×C3⋊D3 | semidirect |
| 185. C33 | #453 | semidirect |
| 242. M16 | C2×C3×C3⋊D3 | semidirect |
| 269. C32 | #4747 | semidirect |
| 270. C32 | C3×#453 | semidirect |
| 310. C3 | C3×#4747 | semidirect |
| 311. C3 | #10592446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64361 | 2 |
| C3×#64149 | 2 |
| C3×#64117 | 2 |
| C33×#100 | 2 |
| C3×#63652 | 2 |
| #10592446 | 3 |
| C3×#4747 | 3 |