Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
244 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 90 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. C32×Dic18 | C2 | semidirect |
| 3. C32×C8×C9 | C2 | semidirect |
| 5. C3×#3664 | C3 | direct (N × H) |
| 13. C3×Dic18 | C2×C3 | semidirect |
| 15. C3×C8×C9 | C2×C3 | semidirect |
| 20. #3664 | C32 | direct (N × H) |
| 28. C32×C9 | SD16 | semidirect |
| 34. C32×C8 | D9 | semidirect |
| 37. Dic18 | C2×C32 | semidirect |
| 39. C8×C9 | C2×C32 | semidirect |
| 60. C3×C9 | C3×SD16 | semidirect |
| 66. C3×C8 | C3×D9 | semidirect |
| 85. C32 | #3664 | direct (N × H) |
| 88. C9 | C32×SD16 | semidirect |
| 91. C8 | C32×D9 | semidirect |
| 101. C3 | C3×#3664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D36 | 2 |
| C32×Dic18 | 2 |
| C32×C8×C9 | 2 |
| C32×#204 | 3 |
| C3×#3664 | 3 |