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. #10619992 | C2 | semidirect |
| 2. C2×C3×C3⋊Dic9 | C2 | semidirect |
| 3. C3×C9×#67 | C2 | semidirect |
| 4. #10619880 | C2 | semidirect |
| 5. D3×C3⋊Dic9 | C2 | semidirect |
| 6. #10619872 | C2 | semidirect |
| 7. #10619868 | C2 | semidirect |
| 32. C2×C3⋊Dic9 | D3 | semidirect |
| 35. C9×#67 | D3 | semidirect |
| 76. C32×C9 | #41 | semidirect |
| 88. C3×#67 | D9 | semidirect |
| 169. C3×C9 | #235 | semidirect |
| 170. C3×C9 | #237 | semidirect |
| 181. #67 | C3⋊D9 | semidirect |
| 249. C32 | #3699 | semidirect |
| 253. C9 | #3804 | semidirect |
| 288. C3 | #88662 | semidirect |
| 289. C3 | #88742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619992 | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| C3×C9×#67 | 2 |
| #10619880 | 2 |
| D3×C3⋊Dic9 | 2 |
| #10619872 | 2 |
| #10619868 | 2 |
| #89028 | 3 |
| #88742 | 3 |
| #88662 | 3 |