Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
549 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 549 conjugacy classes of subgroups — too many to draw. Only its 230 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×#66409 | C2 | direct (N × H) |
| 3. C22×C3⋊Dic9 | C3 | semidirect |
| 7. C22×#737 | C4 | semidirect |
| 9. #66409 | C22 | direct (N × H) |
| 17. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 21. C2×#737 | C2×C4 | semidirect |
| 31. C22×3−1+2 | Dic3 | semidirect |
| 37. C22×C3×C9 | Dic3 | semidirect |
| 38. C22×C3×C9 | C3×C4 | semidirect |
| 41. C3⋊Dic9 | C22×C3 | semidirect |
| 45. #737 | C22×C4 | semidirect |
| 61. C2×3−1+2 | C2×Dic3 | semidirect |
| 67. C2×C3×C9 | C2×Dic3 | semidirect |
| 68. C2×C3×C9 | C2×C3×C4 | semidirect |
| 94. 3−1+2 | C22×Dic3 | semidirect |
| 97. C3×C9 | C22×Dic3 | semidirect |
| 98. C3×C9 | C22×C3×C4 | semidirect |
| 149. C22 | #66409 | direct (N × H) |
| 156. C2 | C2×#66409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#737 | 2 |
| C2×#66409 | 2 |
| C22×C3⋊Dic9 | 3 |
| C22×3−1+2⋊C4 | 3 |
| C22×(C3⋊Dic3)⋊C3 | 3 |
| C22×C3×Dic9 | 3 |