Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
520 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 104 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. C4×C3⋊(C3⋊D9) | C2 | semidirect |
| 2. C3×#6226 | C2 | semidirect |
| 3. C3×C9×D12 | C2 | semidirect |
| 4. #10619880 | C2 | semidirect |
| 5. D3×C3⋊Dic9 | C2 | semidirect |
| 26. #6226 | D3 | semidirect |
| 27. C9×D12 | D3 | semidirect |
| 59. C32×C9 | #41 | semidirect |
| 69. C3×D12 | D9 | semidirect |
| 131. C3×C9 | #237 | semidirect |
| 132. C3×C9 | #239 | semidirect |
| 141. D12 | C3⋊D9 | semidirect |
| 192. C32 | #3699 | semidirect |
| 196. C9 | #3796 | semidirect |
| 222. C3 | #88639 | semidirect |
| 223. C3 | #88742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C3⋊D9) | 2 |
| C3×#6226 | 2 |
| C3×C9×D12 | 2 |
| #10619880 | 2 |
| D3×C3⋊Dic9 | 2 |
| #89015 | 3 |
| #88742 | 3 |
| #88639 | 3 |