Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
204 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 81 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. Q8×C9⋊C9 | C2 | semidirect |
| 2. C4⋊(D9⋊C9) | C2 | semidirect |
| 3. C4×D9⋊C9 | C2 | semidirect |
| 20. #3701 | C9 | semidirect |
| 28. C9⋊C9 | #41 | semidirect |
| 35. Q8×C9 | C2×C9 | semidirect |
| 38. D36 | C2×C9 | semidirect |
| 39. C4×D9 | C2×C9 | semidirect |
| 88. C9 | C9×#41 | semidirect |
| 89. Q8 | D9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9⋊C9 | 2 |
| C4⋊(D9⋊C9) | 2 |
| C4×D9⋊C9 | 2 |
| C9×#239 | 3 |
| C3×#3701 | 3 |