Finite Group DatabasebetaFinite Group Databasebeta← C2×((C3⋊D3)⋊C9)⋊C9 #72244045
Order 2916.
521 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 112 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. ((C3⋊D3)⋊C9)⋊C9 | C2 | direct (N × H) |
| 2. C2×#10624556 | C2 | semidirect |
| 8. #10624556 | C22 | semidirect |
| 12. C2×C3×C9⋊C9 | D3 | semidirect |
| 33. C2×(C3⋊D3)⋊C9 | C9 | semidirect |
| 34. C2×(C3⋊D3)⋊C9 | C9 | semidirect |
| 37. C3×C9⋊C9 | C2×D3 | semidirect |
| 76. C2×C32⋊C9 | C2×C9 | semidirect |
| 77. C2×C32⋊C9 | C2×C9 | semidirect |
| 80. (C3⋊D3)⋊C9 | C2×C9 | semidirect |
| 81. (C3⋊D3)⋊C9 | C2×C9 | semidirect |
| 122. C32⋊C9 | C22×C9 | semidirect |
| 123. C32⋊C9 | C22×C9 | semidirect |
| 178. C2×C3×C9 | D3×C9 | semidirect |
| 179. C2×C3×C9 | D3×C9 | semidirect |
| 188. C2×C3⋊D3 | C9⋊C9 | semidirect |
| 246. C3×C9 | C2×D3×C9 | semidirect |
| 247. C3×C9 | C2×D3×C9 | semidirect |
| 274. C2×C32 | C2×C9⋊C9 | semidirect |
| 280. C3⋊D3 | C2×C9⋊C9 | semidirect |
| 335. C32 | C22×C9⋊C9 | semidirect |
| 388. C2 | ((C3⋊D3)⋊C9)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ((C3⋊D3)⋊C9)⋊C9 | 2 |
| C2×#10624556 | 2 |
| C2×C3×C9×C3⋊D3 | 3 |
| C2×D3×C9⋊C9 | 3 |
| C2×C3×(C3⋊D3)⋊C9 | 3 |