Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
456 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10619898 | C2 | direct (N × H) |
| 7. C2×C9×C3⋊D3 | C4 | semidirect |
| 9. C3×C3⋊Dic9 | C22 | semidirect |
| 15. C2×C3⋊Dic9 | D3 | semidirect |
| 19. C2×C32×C9 | C2×C4 | semidirect |
| 21. C9×C3⋊D3 | C2×C4 | semidirect |
| 37. C3⋊Dic9 | C2×D3 | semidirect |
| 40. C32×C9 | C22×C4 | semidirect |
| 63. C2×C3×C9 | C4×D3 | semidirect |
| 74. C2×C3⋊D3 | Dic9 | semidirect |
| 95. C3×C9 | C2×C4×D3 | semidirect |
| 111. C2×C32 | C2×Dic9 | semidirect |
| 115. C3⋊D3 | C2×Dic9 | semidirect |
| 123. C2×C9 | #624 | semidirect |
| 144. C32 | C22×Dic9 | semidirect |
| 148. C9 | C2×#624 | semidirect |
| 159. C2×C3 | D3×Dic9 | semidirect |
| 172. C3 | C2×D3×Dic9 | semidirect |
| 175. C2 | #10619898 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×C3⋊D3 | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| #10619898 | 2 |
| C2×#6294 | 3 |
| C2×D3×Dic9 | 3 |