Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 347 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. C33×#135 | C2 | semidirect |
| 2. C2×#88852 | C2 | semidirect |
| 3. #11722198 | C2 | semidirect |
| 4. #11722196 | C2 | semidirect |
| 5. #11722182 | C2 | semidirect |
| 9. C33×Q16 | C22 | semidirect |
| 11. C33×D8 | C22 | semidirect |
| 15. C3⋊(C3⋊(C3⋊C16)) | C22 | semidirect |
| 16. C32×#135 | D3 | semidirect |
| 34. C32×Q16 | C2×D3 | semidirect |
| 36. C32×D8 | C2×D3 | semidirect |
| 48. C3×#135 | C3⋊D3 | semidirect |
| 70. C3×Q16 | C2×C3⋊D3 | semidirect |
| 72. C3×D8 | C2×C3⋊D3 | semidirect |
| 84. #135 | C3⋊(C3⋊D3) | semidirect |
| 89. C33 | #509 | semidirect |
| 106. Q16 | C2×C3⋊(C3⋊D3) | semidirect |
| 110. D8 | C2×C3⋊(C3⋊D3) | semidirect |
| 120. C32 | #5193 | semidirect |
| 142. C3 | #10592892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#135 | 2 |
| C2×#88852 | 2 |
| #11722198 | 2 |
| #11722196 | 2 |
| #11722182 | 2 |
| #10592892 | 3 |