Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
469 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 469 conjugacy classes of subgroups — too many to draw. Only its 102 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. C23×C32⋊C9 | C2 | semidirect |
| 2. C22×#4169 | C2 | semidirect |
| 3. #10619630 | C2 | direct (N × H) |
| 4. C2×#66316 | C2 | semidirect |
| 6. C2×#6233 | C3 | semidirect |
| 9. C22×C32⋊C9 | C22 | semidirect |
| 11. C2×#4169 | C22 | semidirect |
| 12. #66316 | C22 | semidirect |
| 18. C23×C3×C9 | C2×C3 | semidirect |
| 19. C22×C3⋊D9 | C2×C3 | semidirect |
| 20. #6233 | C2×C3 | semidirect |
| 21. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 23. C2×C32⋊C9 | D4 | semidirect |
| 42. C22×C3×C9 | C22×C3 | semidirect |
| 44. C2×C3⋊D9 | C22×C3 | semidirect |
| 45. C3⋊Dic9 | C22×C3 | semidirect |
| 46. C32⋊C9 | C2×D4 | semidirect |
| 50. C23×C32 | D9 | semidirect |
| 77. C2×C3×C9 | C3×D4 | semidirect |
| 96. C22×C32 | C2×D9 | semidirect |
| 122. C3×C9 | C2×C3×D4 | semidirect |
| 151. C2×C32 | #611 | semidirect |
| 197. C32 | C2×#611 | semidirect |
| 202. C23 | #4169 | semidirect |
| 228. C22 | C2×#4169 | semidirect |
| 237. C2 | #10619630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32⋊C9 | 2 |
| C22×#4169 | 2 |
| #10619630 | 2 |
| C2×#66316 | 2 |
| C2×C3×#638 | 3 |
| C2×#6233 | 3 |