Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1090 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1090 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×C9×D12 | C2 | semidirect |
| 2. C22×C3×D36 | C2 | semidirect |
| 3. C22×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. C2×#88421 | C2 | direct (N × H) |
| 11. C2×C9×D12 | C22 | semidirect |
| 13. C2×C3×D36 | C22 | semidirect |
| 14. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 15. #88421 | C22 | direct (N × H) |
| 21. C22×D36 | D3 | semidirect |
| 33. C9×D12 | C23 | semidirect |
| 35. C3×D36 | C23 | semidirect |
| 36. C3⋊(C9⋊C8) | C23 | semidirect |
| 55. C2×D36 | C2×D3 | semidirect |
| 59. C22×C3×C9 | D8 | semidirect |
| 70. C22×D12 | D9 | semidirect |
| 101. D36 | C22×D3 | semidirect |
| 105. C2×C3×C9 | C2×D8 | semidirect |
| 123. C2×D12 | C2×D9 | semidirect |
| 141. C22×C9 | #213 | semidirect |
| 153. C3×C9 | C22×D8 | semidirect |
| 178. D12 | C22×D9 | semidirect |
| 189. C2×C9 | C2×#213 | semidirect |
| 207. C22×C3 | #3673 | semidirect |
| 223. C9 | C22×#213 | semidirect |
| 240. C2×C3 | C2×#3673 | semidirect |
| 250. C22 | #88421 | direct (N × H) |
| 255. C3 | C22×#3673 | semidirect |
| 259. C2 | C2×#88421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D12 | 2 |
| C22×C3×D36 | 2 |
| C22×C3⋊(C9⋊C8) | 2 |
| C2×#88421 | 2 |
| C22×#3713 | 3 |
| C22×#3673 | 3 |