Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
970 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 970 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 |
|---|---|---|
| 2. C22×C3×Dic18 | C2 | semidirect |
| 3. C22×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. C2×#88423 | C2 | direct (N × H) |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 14. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 15. #88423 | C22 | direct (N × H) |
| 21. C22×Dic18 | D3 | semidirect |
| 34. C3×Dic18 | C23 | semidirect |
| 35. C3⋊(C9⋊C8) | C23 | semidirect |
| 54. C2×Dic18 | C2×D3 | semidirect |
| 58. C22×C3×C9 | SD16 | semidirect |
| 97. Dic18 | C22×D3 | semidirect |
| 101. C2×C3×C9 | C2×SD16 | semidirect |
| 135. C22×C9 | #215 | semidirect |
| 146. C3×C9 | C22×SD16 | semidirect |
| 179. C2×C9 | C2×#215 | semidirect |
| 194. C22×C3 | #3672 | semidirect |
| 210. C9 | C22×#215 | semidirect |
| 225. C2×C3 | C2×#3672 | semidirect |
| 232. C22 | #88423 | direct (N × H) |
| 238. C3 | C22×#3672 | semidirect |
| 241. C2 | C2×#88423 | 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×Dic18 | 2 |
| C22×C3⋊(C9⋊C8) | 2 |
| C2×#88423 | 2 |
| C22×#3715 | 3 |
| C22×#3672 | 3 |