Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 405 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. C2×#88853 | C2 | semidirect |
| 4. C33×#106 | C2 | semidirect |
| 5. #11722180 | C2 | semidirect |
| 19. C32×#106 | D3 | semidirect |
| 53. C3×#106 | C3⋊D3 | semidirect |
| 90. #106 | C3⋊(C3⋊D3) | semidirect |
| 92. C33 | #470 | semidirect |
| 124. C32 | #4867 | semidirect |
| 147. C3 | #10592566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88853 | 2 |
| C2×#88850 | 2 |
| #11723938 | 2 |
| C33×#106 | 2 |
| #11722180 | 2 |
| #10592566 | 3 |