Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
891 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 891 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 |
|---|---|---|
| 2. C3×#5798 | C2 | semidirect |
| 3. C2×C3×#833 | C2 | semidirect |
| 4. #10591113 | C2 | semidirect |
| 5. #10589158 | C2 | semidirect |
| 11. #64149 | C4 | semidirect |
| 13. #64145 | C4 | semidirect |
| 25. #5798 | D3 | semidirect |
| 27. C2×#833 | D3 | semidirect |
| 42. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 44. C2×#634 | C2×C4 | semidirect |
| 49. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 53. C3×C4×Dic3 | D4 | semidirect |
| 182. C4×Dic3 | #67 | semidirect |
| 355. C32 | #1911 | semidirect |
| 413. C3 | #70071 | semidirect |
| 414. C3 | #71652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596276 | 2 |
| C3×#5798 | 2 |
| C2×C3×#833 | 2 |
| #10591113 | 2 |
| #10589158 | 2 |
| #71652 | 3 |
| #70071 | 3 |