Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
195 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 3. Dic18⋊C9 | C2 | semidirect |
| 17. D9⋊C9 | Q8 | direct (N × H) |
| 20. Q8×D9 | C9 | semidirect |
| 28. C9⋊C9 | C2×Q8 | semidirect |
| 36. Q8×C9 | C2×C9 | semidirect |
| 39. Dic18 | C2×C9 | semidirect |
| 75. D9 | Q8×C9 | semidirect |
| 88. C9 | C2×Q8×C9 | semidirect |
| 90. Q8 | D9⋊C9 | direct (N × H) |
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 |
| Dic18⋊C9 | 2 |
| D3×Q8×C9 | 3 |
| C3×Q8×D9 | 3 |