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×C4×D3×C9 | C2 | semidirect |
| 4. #10619880 | C2 | semidirect |
| 5. #10619872 | C2 | semidirect |
| 26. #6226 | D3 | semidirect |
| 27. C4×D3×C9 | D3 | semidirect |
| 57. C32×C9 | #41 | semidirect |
| 67. C3×C4×D3 | D9 | semidirect |
| 126. C3×C9 | #235 | semidirect |
| 127. C3×C9 | #239 | semidirect |
| 142. C4×D3 | C3⋊D9 | semidirect |
| 185. C32 | #3697 | semidirect |
| 189. C9 | #3799 | semidirect |
| 215. C3 | #88642 | semidirect |
| 216. C3 | #88736 | 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×C4×D3×C9 | 2 |
| #10619880 | 2 |
| #10619872 | 2 |
| #89022 | 3 |
| #88736 | 3 |
| #88642 | 3 |