Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 407 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×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. #11723936 | C2 | semidirect |
| 4. C33×#107 | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 19. C32×#107 | D3 | semidirect |
| 31. C33×C8 | D4 | semidirect |
| 49. C2×C3⋊(C3⋊D3) | D8 | semidirect |
| 57. C3×#107 | C3⋊D3 | semidirect |
| 69. C32×C8 | D12 | semidirect |
| 100. #107 | C3⋊(C3⋊D3) | semidirect |
| 102. C33 | #466 | semidirect |
| 113. C3×C8 | C4⋊(C3⋊D3) | semidirect |
| 140. C32 | #4883 | semidirect |
| 152. C8 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 169. C3 | #10592582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88852 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723936 | 2 |
| C33×#107 | 2 |
| #11722179 | 2 |
| #10592582 | 3 |