Finite Group DatabasebetaFinite Group Databasebeta← C2×((C3⋊D3)⋊C9)⋊C4 #13047162
Order 1296.
345 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 345 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 |
|---|---|---|
| 2. C2×#66328 | C2 | semidirect |
| 3. C2×#66316 | C2 | semidirect |
| 4. ((C3⋊D3)⋊C9)⋊C4 | C2 | direct (N × H) |
| 8. C2×(C3⋊D3)⋊C9 | C4 | semidirect |
| 10. #66328 | C22 | semidirect |
| 11. #66316 | C22 | semidirect |
| 17. C2×C3⋊Dic9 | D3 | semidirect |
| 21. C2×C32⋊C9 | C2×C4 | semidirect |
| 23. (C3⋊D3)⋊C9 | C2×C4 | semidirect |
| 37. C3⋊Dic9 | C2×D3 | semidirect |
| 40. C32⋊C9 | C22×C4 | semidirect |
| 65. C2×C3×C9 | C4×D3 | semidirect |
| 76. C2×C3⋊D3 | Dic9 | semidirect |
| 99. C3×C9 | C2×C4×D3 | semidirect |
| 120. C2×C32 | C2×Dic9 | semidirect |
| 124. C3⋊D3 | C2×Dic9 | semidirect |
| 155. C32 | C22×Dic9 | semidirect |
| 187. C2 | ((C3⋊D3)⋊C9)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊C9 | 2 |
| C2×#66328 | 2 |
| C2×#66316 | 2 |
| ((C3⋊D3)⋊C9)⋊C4 | 2 |
| C2×#6294 | 3 |
| C2×D3×Dic9 | 3 |