Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
587 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 587 conjugacy classes of subgroups — too many to draw. Only its 126 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. C23×#737 | C2 | semidirect |
| 2. C22×#4208 | C2 | semidirect |
| 3. #10619984 | C2 | direct (N × H) |
| 4. C2×#66410 | C2 | semidirect |
| 9. C22×#737 | C22 | semidirect |
| 11. C2×#4208 | C22 | semidirect |
| 12. #66410 | C22 | semidirect |
| 15. C23×C3×C9 | D3 | semidirect |
| 23. C2×#737 | D4 | semidirect |
| 36. C22×C3×C9 | C2×D3 | semidirect |
| 43. #737 | C2×D4 | semidirect |
| 60. C2×C3×C9 | #67 | semidirect |
| 83. C3×C9 | C2×#67 | semidirect |
| 120. C23 | #4208 | semidirect |
| 135. C22 | C2×#4208 | semidirect |
| 141. C2 | #10619984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#737 | 2 |
| C22×#4208 | 2 |
| #10619984 | 2 |
| C2×#66410 | 2 |
| C2×#6235 | 3 |
| C2×C9×#67 | 3 |