Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
411 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#66437 | C2 | semidirect |
| 2. #10620072 | C2 | direct (N × H) |
| 6. #66437 | C22 | semidirect |
| 13. C2×C3×C22⋊C9 | D3 | semidirect |
| 30. C3×C22⋊C9 | C2×D3 | semidirect |
| 109. C23 | #4208 | semidirect |
| 128. C22 | C2×#4208 | semidirect |
| 135. C2 | #10620072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66437 | 2 |
| #10620072 | 2 |
| C23×#272 | 3 |
| C2×D3×C22⋊C9 | 3 |
| C2×#4208 | 4 |