Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
302 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 302 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. C23×#731 | C2 | semidirect |
| 2. C22×#4177 | C2 | semidirect |
| 3. #10619646 | C2 | direct (N × H) |
| 4. C2×#66324 | C2 | semidirect |
| 5. C2×#6233 | C3 | semidirect |
| 9. C22×#731 | C22 | semidirect |
| 11. C2×#4177 | C22 | semidirect |
| 12. #66324 | C22 | semidirect |
| 15. C23×C3×C9 | C2×C3 | semidirect |
| 16. C22×C3⋊D9 | C2×C3 | semidirect |
| 18. #6233 | C2×C3 | semidirect |
| 19. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 23. C2×#731 | D4 | semidirect |
| 37. C22×C3×C9 | C22×C3 | semidirect |
| 39. C2×C3⋊D9 | C22×C3 | semidirect |
| 42. C3⋊Dic9 | C22×C3 | semidirect |
| 44. #731 | C2×D4 | semidirect |
| 65. C2×C3×C9 | C3×D4 | semidirect |
| 95. C3×C9 | C2×C3×D4 | semidirect |
| 147. C23 | #4177 | semidirect |
| 166. C22 | C2×#4177 | semidirect |
| 173. C2 | #10619646 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#731 | 2 |
| C22×#4177 | 2 |
| #10619646 | 2 |
| C2×#66324 | 2 |
| C2×#6233 | 3 |
| C2×#638⋊C3 | 3 |