Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
762 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×C32⋊(C22⋊C9) | C2 | direct (N × H) |
| 3. C22×C3×C22⋊C9 | C3 | semidirect |
| 5. C32⋊(C22⋊C9) | C22 | direct (N × H) |
| 9. C2×C3×C22⋊C9 | C2×C3 | semidirect |
| 13. C24×C32 | C9 | semidirect |
| 23. C3×C22⋊C9 | C22×C3 | semidirect |
| 35. C23×C32 | C2×C9 | semidirect |
| 66. C22×C32 | C22⋊C9 | semidirect |
| 67. C22×C32 | C22×C9 | semidirect |
| 96. C2×C32 | C2×C22⋊C9 | semidirect |
| 99. C24 | C32⋊C9 | semidirect |
| 126. C32 | C22×C22⋊C9 | semidirect |
| 131. C23 | C2×C32⋊C9 | semidirect |
| 148. C22 | C32⋊(C22⋊C9) | direct (N × H) |
| 149. C22 | C22×C32⋊C9 | semidirect |
| 156. C2 | C2×C32⋊(C22⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32⋊(C22⋊C9) | 2 |
| C24×C33 | 3 |
| C22×C3×C22⋊C9 | 3 |
| C22×C32⋊C9 | 4 |