Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4732 conjugacy classes of subgroups; only the 931 normal subgroups are shown.
This group has 4732 conjugacy classes of subgroups — too many to draw. Only its 931 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×#117 | C2 | semidirect |
| 3. #11723967 | C2 | semidirect |
| 4. #11723934 | C2 | semidirect |
| 5. C22⋊C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 6. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 10. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 13. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 14. C33×C4⋊C4 | C22 | semidirect |
| 16. C33×C42 | C22 | semidirect |
| 18. #88859 | C22 | semidirect |
| 19. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 20. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 22. C32×#117 | D3 | semidirect |
| 29. C22×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 31. C2×C33×C4 | C2×C4 | semidirect |
| 36. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 37. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 46. C32×C4⋊C4 | C2×D3 | semidirect |
| 48. C32×C42 | C2×D3 | semidirect |
| 64. C3×#117 | C3⋊D3 | semidirect |
| 73. C2×C32×C4 | C4×D3 | semidirect |
| 92. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 94. C3×C42 | C2×C3⋊D3 | semidirect |
| 113. #117 | C3⋊(C3⋊D3) | semidirect |
| 115. C33 | #518 | semidirect |
| 120. C2×C3×C4 | C4×C3⋊D3 | semidirect |
| 139. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 144. C42 | C2×C3⋊(C3⋊D3) | semidirect |
| 155. C32 | #5521 | semidirect |
| 164. C2×C4 | C4×C3⋊(C3⋊D3) | semidirect |
| 182. C3 | #10595992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×#117 | 2 |
| #11723967 | 2 |
| #11723934 | 2 |
| C22⋊C4×C3⋊(C3⋊D3) | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #10595992 | 3 |