Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1820 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1820 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×#88852 | C2 | semidirect |
| 2. C2×#88850 | C2 | semidirect |
| 3. #11723936 | C2 | semidirect |
| 4. C33×#106 | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 19. C32×#106 | D3 | semidirect |
| 31. C33×C8 | D4 | semidirect |
| 56. C3×#106 | C3⋊D3 | semidirect |
| 68. C32×C8 | D12 | semidirect |
| 97. #106 | C3⋊(C3⋊D3) | semidirect |
| 99. C33 | #469 | semidirect |
| 110. C3×C8 | C4⋊(C3⋊D3) | semidirect |
| 135. C32 | #4865 | semidirect |
| 147. C8 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 162. C3 | #10592564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| C2×#88850 | 2 |
| #11723936 | 2 |
| C33×#106 | 2 |
| #11722179 | 2 |
| #10592564 | 3 |