Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2660 conjugacy classes of subgroups; only the 639 normal subgroups are shown.
This group has 2660 conjugacy classes of subgroups — too many to draw. Only its 639 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. C2×C33×M16 | C2 | semidirect |
| 3. C2×#88855 | C2 | semidirect |
| 4. #11722190 | C2 | semidirect |
| 14. C2×C33×C8 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 18. C2×C32×M16 | D3 | semidirect |
| 45. C2×C32×C8 | C2×D3 | semidirect |
| 54. C2×C3⋊(C3⋊D3) | M16 | semidirect |
| 60. C2×C3×M16 | C3⋊D3 | semidirect |
| 91. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 107. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 109. C33 | #407 | semidirect |
| 139. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 151. C32 | #5126 | semidirect |
| 182. C3 | #10592825 | 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 |
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| #11722190 | 2 |
| #10592825 | 3 |