Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
294 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×#4178 | C2 | semidirect |
| 2. C2×C4×#732 | C2 | semidirect |
| 3. C4⋊#4178 | C2 | direct (N × H) |
| 4. C2×C4⋊#272 | C3 | semidirect |
| 8. C2×#4178 | C22 | semidirect |
| 9. C4×#732 | C22 | semidirect |
| 14. C2×C3×C4×C9 | D3 | semidirect |
| 15. C4⋊#272 | C2×C3 | semidirect |
| 17. C2×#732 | D4 | semidirect |
| 32. C3×C4×C9 | C2×D3 | semidirect |
| 33. #732 | C2×D4 | semidirect |
| 48. C2×C3×C9 | D12 | semidirect |
| 71. C3×C9 | C2×D12 | semidirect |
| 114. C2×C4 | #4178 | semidirect |
| 129. C4 | C2×#4178 | semidirect |
| 135. C2 | C4⋊#4178 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4178 | 2 |
| C2×C4×#732 | 2 |
| C4⋊#4178 | 2 |
| C2×C4⋊#272 | 3 |
| C2×C9×D12 | 3 |