Finite Group DatabasebetaFinite Group Databasebeta← C2×((C22⋊C9)⋊C2)⋊C9 #13048101
Order 1296.
192 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 35 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×(C22⋊C9)⋊C9 | C2 | semidirect |
| 2. ((C22⋊C9)⋊C2)⋊C9 | C2 | direct (N × H) |
| 6. (C22⋊C9)⋊C9 | C22 | semidirect |
| 18. C2×(C22⋊C9)⋊C2 | C9 | semidirect |
| 40. C2×C22⋊C9 | C2×C9 | semidirect |
| 41. (C22⋊C9)⋊C2 | C2×C9 | semidirect |
| 72. C22⋊C9 | C22×C9 | semidirect |
| 126. C23 | D9⋊C9 | semidirect |
| 146. C22 | C2×D9⋊C9 | semidirect |
| 154. C2 | ((C22⋊C9)⋊C2)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C22⋊C9)⋊C9 | 2 |
| ((C22⋊C9)⋊C2)⋊C9 | 2 |
| C2×C3×(C22⋊C9)⋊C2 | 3 |
| C2×C9×#67 | 3 |
| C2×D9⋊C9 | 4 |