Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10590807 | C2 | semidirect |
| 4. C3×#4504 | C2 | semidirect |
| 5. C3×#4502 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 15. #63627 | C4 | semidirect |
| 32. #4504 | D3 | semidirect |
| 34. #4502 | D3 | semidirect |
| 42. #3746 | C2×C4 | semidirect |
| 52. C32×C16 | C2×C4 | semidirect |
| 144. C3×C16 | C4×D3 | semidirect |
| 145. C3×C16 | C4×D3 | semidirect |
| 229. C16 | #624 | semidirect |
| 259. C32 | #2175 | semidirect |
| 299. C3 | #69077 | semidirect |
| 300. C3 | #69319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| #10590807 | 2 |
| #10590763 | 2 |
| C3×#4504 | 2 |
| C3×#4502 | 2 |
| #10589119 | 2 |
| #10589116 | 2 |
| #69319 | 3 |
| #69077 | 3 |