Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1205 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1205 conjugacy classes of subgroups — too many to draw. Only its 244 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×#4936 | C2 | semidirect |
| 4. #10591378 | C2 | semidirect |
| 5. #10591273 | C2 | semidirect |
| 6. #10591266 | C2 | semidirect |
| 13. #64084 | C4 | semidirect |
| 28. #4936 | D3 | semidirect |
| 42. C2×#634 | C2×C4 | semidirect |
| 47. C32×C42 | C2×C4 | semidirect |
| 48. #3752 | C2×C4 | semidirect |
| 144. C3×C42 | C4×D3 | semidirect |
| 264. C42 | #624 | semidirect |
| 300. C32 | #2379 | semidirect |
| 355. C3 | #74230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64084 | 2 |
| C3×#4936 | 2 |
| #10591380 | 2 |
| #10591378 | 2 |
| #10591273 | 2 |
| #10591266 | 2 |
| #74230 | 3 |