Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
786 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 157 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. C32×#413 | C2 | semidirect |
| 3. #10592936 | C2 | semidirect |
| 4. #10589343 | C2 | semidirect |
| 17. C32×#101 | C22 | semidirect |
| 19. #63663 | C22 | semidirect |
| 22. C3×#413 | D3 | semidirect |
| 64. C3×#101 | C2×D3 | semidirect |
| 98. #413 | C3⋊D3 | semidirect |
| 156. #101 | C2×C3⋊D3 | semidirect |
| 237. C32 | #2134 | semidirect |
| 289. C3 | #70149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596301 | 2 |
| C32×#413 | 2 |
| #10592936 | 2 |
| #10589343 | 2 |
| #70149 | 3 |