Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
470 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #10619867 | C2 | direct (N × H) |
| 20. C2×C32×C9 | Q8 | semidirect |
| 35. C32×C9 | C2×Q8 | semidirect |
| 54. C2×C3×C9 | Dic6 | semidirect |
| 76. C3×C9 | C2×Dic6 | semidirect |
| 88. C2×C32 | Dic18 | semidirect |
| 94. C2×C9 | #634 | semidirect |
| 108. C32 | C2×Dic18 | semidirect |
| 111. C9 | C2×#634 | semidirect |
| 118. C2×C3 | #6189 | semidirect |
| 127. C3 | C2×#6189 | semidirect |
| 129. C2 | #10619867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊Dic9) | 2 |
| C2×C9×C3⋊Dic3 | 2 |
| C2×C32×Dic9 | 2 |
| #10619867 | 2 |
| C2×#6293 | 3 |
| C2×#6189 | 3 |