Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
470 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 91 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. C9×#634 | C2 | semidirect |
| 3. C32×Dic18 | C2 | semidirect |
| 5. #10619867 | C2 | semidirect |
| 21. C3×Dic18 | D3 | semidirect |
| 25. C3⋊(C3⋊D9) | Q8 | semidirect |
| 42. C32×C9 | C2×Q8 | semidirect |
| 49. #634 | D9 | semidirect |
| 59. Dic18 | C3⋊D3 | semidirect |
| 91. C3×C9 | D3×Q8 | semidirect |
| 128. C32 | Q8×D9 | semidirect |
| 131. C9 | Q8×C3⋊D3 | semidirect |
| 149. C3 | (C3⋊D9)⋊Q8 | 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 |
| C9×#634 | 2 |
| C32×Dic18 | 2 |
| #10619870 | 2 |
| #10619867 | 2 |
| #89019 | 3 |
| (C3⋊D9)⋊Q8 | 3 |