Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
784 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 2. C3×#568⋊C3 | C2 | semidirect |
| 3. C2×C3×#131⋊C3 | C2 | semidirect |
| 4. C3×#3573 | C3 | semidirect |
| 5. #85629 | C3 | direct (N × H) |
| 10. C3×#131⋊C3 | C22 | semidirect |
| 11. C3×#131⋊C3 | C22 | semidirect |
| 16. C3×#568 | C2×C3 | semidirect |
| 19. C2×C3×#131 | C2×C3 | semidirect |
| 20. #568⋊C3 | C2×C3 | semidirect |
| 21. C2×#131⋊C3 | C2×C3 | semidirect |
| 28. #3573 | C32 | semidirect |
| 56. #131⋊C3 | C22×C3 | semidirect |
| 57. #131⋊C3 | C22×C3 | semidirect |
| 67. #568 | C2×C32 | semidirect |
| 70. C2×#131 | C2×C32 | semidirect |
| 250. C3 | #85629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5945 | 2 |
| C3×#568⋊C3 | 2 |
| C2×C3×#131⋊C3 | 2 |
| C3×#3573 | 3 |
| #85629 | 3 |
| C32×#131 | 4 |