Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2660 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2660 conjugacy classes of subgroups — too many to draw. Only its 635 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. C2×#88855 | C2 | semidirect |
| 4. #11722179 | C2 | semidirect |
| 10. C2×C4⋊(C3⋊(C3⋊D3)) | C4 | semidirect |
| 12. C33×C4⋊C4 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 18. C32×#117 | D3 | semidirect |
| 41. C32×C4⋊C4 | C2×D3 | semidirect |
| 57. C3×#117 | C3⋊D3 | semidirect |
| 84. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 101. #117 | C3⋊(C3⋊D3) | semidirect |
| 103. C33 | #418 | semidirect |
| 129. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 142. C32 | #5001 | semidirect |
| 170. C3 | #10592700 | 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 |
| C2×#88855 | 2 |
| #11722179 | 2 |
| #10592700 | 3 |