Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3724 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3724 conjugacy classes of subgroups — too many to draw. Only its 891 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×#89076 | C2 | semidirect |
| 2. C22×C33×C8 | C2 | semidirect |
| 3. C2×#88853 | C2 | semidirect |
| 4. #11723945 | C2 | direct (N × H) |
| 5. C2×#88852 | C2 | semidirect |
| 6. C2×#88851 | C2 | semidirect |
| 11. #89076 | C22 | semidirect |
| 17. C2×C33×C8 | C22 | semidirect |
| 18. #88853 | C22 | semidirect |
| 19. #88852 | C22 | semidirect |
| 20. #88851 | C22 | semidirect |
| 22. C22×C32×C8 | D3 | semidirect |
| 52. C2×C32×C8 | C2×D3 | semidirect |
| 66. C22×C3×C8 | C3⋊D3 | semidirect |
| 88. C2×C33 | #135 | semidirect |
| 100. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 118. C22×C8 | C3⋊(C3⋊D3) | semidirect |
| 119. C33 | C2×#135 | semidirect |
| 136. C2×C32 | #904 | semidirect |
| 151. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 161. C32 | C2×#904 | semidirect |
| 178. C2×C3 | #64113 | semidirect |
| 190. C3 | C2×#64113 | semidirect |
| 193. C2 | #11723945 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C22×C33×C8 | 2 |
| C2×#88853 | 2 |
| #11723945 | 2 |
| C2×#88852 | 2 |
| C2×#88851 | 2 |
| C2×#64113 | 3 |