Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1050 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 257 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. C22×#6226 | C2 | semidirect |
| 3. C22×C3×C9⋊C8 | C2 | semidirect |
| 4. C2×#88424 | C2 | direct (N × H) |
| 11. C2×#6226 | C22 | semidirect |
| 14. C2×C3×C9⋊C8 | C22 | semidirect |
| 15. #88424 | C22 | direct (N × H) |
| 24. C22×C9⋊C8 | D3 | semidirect |
| 32. #6226 | C23 | semidirect |
| 35. C3×C9⋊C8 | C23 | semidirect |
| 59. C2×C9⋊C8 | C2×D3 | semidirect |
| 60. C22×C3×C9 | SD16 | semidirect |
| 103. C9⋊C8 | C22×D3 | semidirect |
| 105. C2×C3×C9 | C2×SD16 | semidirect |
| 141. C22×C9 | #204 | semidirect |
| 153. C3×C9 | C22×SD16 | semidirect |
| 188. C2×C9 | C2×#204 | semidirect |
| 203. C22×C3 | #3672 | semidirect |
| 220. C9 | C22×#204 | semidirect |
| 235. C2×C3 | C2×#3672 | semidirect |
| 242. C22 | #88424 | direct (N × H) |
| 248. C3 | C22×#3672 | semidirect |
| 251. C2 | C2×#88424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C22×C9×D12 | 2 |
| C22×C3×C9⋊C8 | 2 |
| C2×#88424 | 2 |
| C22×#3716 | 3 |
| C22×#3672 | 3 |