Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4004 conjugacy classes of subgroups; only the 971 normal subgroups are shown.
This group has 4004 conjugacy classes of subgroups — too many to draw. Only its 971 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. C23×C33×C4 | C2 | semidirect |
| 3. C2×#88864 | C2 | semidirect |
| 4. C2×#88859 | C2 | semidirect |
| 5. #11722201 | C2 | semidirect |
| 14. C2×#6312 | C4 | semidirect |
| 19. C23×C32×C4 | D3 | semidirect |
| 34. C22×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 38. C2×C33×C4 | D4 | semidirect |
| 45. C2×C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 63. C22×C33 | C22⋊C4 | semidirect |
| 77. C23×C3×C4 | C3⋊D3 | semidirect |
| 96. C2×C32×C4 | #67 | semidirect |
| 128. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 143. C23×C4 | C3⋊(C3⋊D3) | semidirect |
| 147. C33 | #386 | semidirect |
| 162. C2×C3×C4 | #638 | semidirect |
| 193. C22×C3 | #3752 | semidirect |
| 207. C32 | #5213 | semidirect |
| 229. C2×C4 | #6312 | semidirect |
| 246. C22 | #88859 | semidirect |
| 255. C3 | #10592912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C22×#6312 | 2 |
| C2×#88864 | 2 |
| C2×#88859 | 2 |
| #11722201 | 2 |
| #10592912 | 3 |