Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
523 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 523 conjugacy classes of subgroups — too many to draw. Only its 104 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×#4208 | C2 | semidirect |
| 2. D4×#737 | C2 | semidirect |
| 3. #10619984 | C2 | semidirect |
| 4. C4⋊#4208 | C2 | semidirect |
| 5. C4×#4208 | C2 | semidirect |
| 8. C22×#737 | C22 | semidirect |
| 11. C2×#4208 | C22 | semidirect |
| 12. C4×#737 | C22 | semidirect |
| 13. #66410 | C22 | semidirect |
| 18. C3×D4×C9 | D3 | semidirect |
| 28. #4208 | D4 | direct (N × H) |
| 33. C22×C3×C9 | C2×D3 | semidirect |
| 42. C3×C4×C9 | C2×D3 | semidirect |
| 45. #737 | C2×D4 | semidirect |
| 85. C3×C9 | D3×D4 | semidirect |
| 125. D4 | #4208 | direct (N × H) |
| 138. C22 | C2×#4208 | semidirect |
| 140. C4 | C2×#4208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4208 | 2 |
| D4×#737 | 2 |
| #10619984 | 2 |
| C4⋊#4208 | 2 |
| C4×#4208 | 2 |
| D4×#272 | 3 |
| D3×D4×C9 | 3 |