Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
241 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 72 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. C32×Q8⋊C9 | C2 | semidirect |
| 4. D3×Q8⋊C9 | C3 | direct (N × H) |
| 11. C3×Q8⋊C9 | D3 | direct (N × H) |
| 12. C3×Q8⋊C9 | C2×C3 | semidirect |
| 16. C3×D3×Q8 | C9 | semidirect |
| 28. C32×Q8 | C2×C9 | semidirect |
| 37. Q8⋊C9 | C3×D3 | direct (N × H) |
| 48. D3×Q8 | C3×C9 | semidirect |
| 70. C3×Q8 | D3×C9 | semidirect |
| 71. C3×Q8 | C2×C3×C9 | semidirect |
| 83. C3×D3 | Q8⋊C9 | direct (N × H) |
| 102. C32 | C2×Q8⋊C9 | semidirect |
| 108. Q8 | C3×D3×C9 | semidirect |
| 117. D3 | C3×Q8⋊C9 | direct (N × H) |
| 123. C3 | D3×Q8⋊C9 | direct (N × H) |
| 124. C3 | C2×C3×Q8⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8⋊C9 | 2 |
| C32×D3×Q8 | 3 |
| C2×C3×Q8⋊C9 | 3 |
| D3×Q8⋊C9 | 3 |
| C2×C3×D3×C9 | 4 |