Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
742 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10594703 | C2 | semidirect |
| 2. #10592600 | C2 | semidirect |
| 3. C2×C3×Dic24 | C2 | semidirect |
| 4. C3×#4904 | C2 | semidirect |
| 5. #10590636 | C2 | semidirect |
| 6. #10590246 | C2 | semidirect |
| 7. #10590244 | C2 | semidirect |
| 8. #10590240 | C2 | semidirect |
| 42. C2×Dic24 | D3 | semidirect |
| 43. #4904 | D3 | semidirect |
| 312. C32 | #3417 | semidirect |
| 352. C3 | #82028 | semidirect |
| 353. C3 | #82033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594703 | 2 |
| #10592600 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4904 | 2 |
| #10590636 | 2 |
| #10590246 | 2 |
| #10590244 | 2 |
| #10590240 | 2 |
| #82033 | 3 |
| #82028 | 3 |