Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
122 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 57 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. (C9⋊C8)⋊C9 | C2 | semidirect |
| 17. #3667 | C9 | semidirect |
| 27. C9⋊C9 | M16 | semidirect |
| 35. C9⋊C8 | C2×C9 | semidirect |
| 91. C9 | C9×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9⋊C9 | 2 |
| (C9⋊C8)⋊C9 | 2 |
| C9×#208 | 3 |
| C3×#3667 | 3 |