Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
780 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 152 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. C2×C3×C3⋊Dic9 | C2 | semidirect |
| 3. C2×C3×C9×Dic3 | C2 | semidirect |
| 4. #10619872 | C2 | direct (N × H) |
| 9. C2×C3⋊(C3⋊D9) | C4 | semidirect |
| 11. C3×C3⋊Dic9 | C22 | semidirect |
| 12. C3×C9×Dic3 | C22 | semidirect |
| 22. C2×C3⋊Dic9 | D3 | semidirect |
| 24. C2×C9×Dic3 | D3 | semidirect |
| 27. C2×C32×C9 | C2×C4 | semidirect |
| 29. C3⋊(C3⋊D9) | C2×C4 | semidirect |
| 52. C3⋊Dic9 | C2×D3 | semidirect |
| 53. C9×Dic3 | C2×D3 | semidirect |
| 55. C32×C9 | C22×C4 | semidirect |
| 66. C2×C3×Dic3 | D9 | semidirect |
| 82. C2×C3×C9 | C4×D3 | semidirect |
| 83. C2×C3×C9 | C4×D3 | semidirect |
| 112. C3×Dic3 | C2×D9 | semidirect |
| 125. C3×C9 | C2×C4×D3 | semidirect |
| 126. C3×C9 | C2×C4×D3 | semidirect |
| 137. C2×Dic3 | C3⋊D9 | semidirect |
| 145. C2×C32 | C4×D9 | semidirect |
| 158. C2×C9 | #624 | semidirect |
| 183. Dic3 | C2×C3⋊D9 | semidirect |
| 186. C32 | C2×C4×D9 | semidirect |
| 190. C9 | C2×#624 | semidirect |
| 199. C2×C3 | (C3⋊D9)⋊C4 | semidirect |
| 200. C2×C3 | C4×C3⋊D9 | semidirect |
| 217. C3 | C2×(C3⋊D9)⋊C4 | semidirect |
| 218. C3 | C2×C4×C3⋊D9 | semidirect |
| 221. C2 | #10619872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊D9) | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| C2×C3×C9×Dic3 | 2 |
| #10619872 | 2 |
| C2×#6289 | 3 |
| C2×C4×C3⋊D9 | 3 |
| C2×(C3⋊D9)⋊C4 | 3 |