Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3612 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 |
|---|---|---|
| 2. C22×#6308 | C2 | semidirect |
| 3. C2×C33×M16 | C2 | semidirect |
| 4. #11723950 | C2 | direct (N × H) |
| 5. C2×#88853 | C2 | semidirect |
| 6. C2×#88851 | C2 | semidirect |
| 19. C2×#6308 | C22 | semidirect |
| 20. C33×M16 | C22 | semidirect |
| 22. #88853 | C22 | semidirect |
| 23. #88851 | C22 | semidirect |
| 26. C2×C32×M16 | D3 | semidirect |
| 62. C32×M16 | C2×D3 | semidirect |
| 78. C2×C3×M16 | C3⋊D3 | semidirect |
| 103. C2×C33 | #137 | semidirect |
| 118. C3×M16 | C2×C3⋊D3 | semidirect |
| 137. C2×M16 | C3⋊(C3⋊D3) | semidirect |
| 138. C33 | C2×#137 | semidirect |
| 159. C2×C32 | #909 | semidirect |
| 176. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 188. C32 | C2×#909 | semidirect |
| 209. C2×C3 | #64118 | semidirect |
| 222. C3 | C2×#64118 | semidirect |
| 225. C2 | #11723950 | 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×#6308 | 2 |
| C2×C33×M16 | 2 |
| #11723950 | 2 |
| C2×#88853 | 2 |
| C2×#88851 | 2 |
| C2×#64118 | 3 |