Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2220 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 2220 conjugacy classes of subgroups — too many to draw. Only its 393 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. C2×#64102 | C2 | semidirect |
| 3. C32×#382 | C2 | semidirect |
| 4. #10592687 | C2 | semidirect |
| 5. #10592631 | C2 | semidirect |
| 6. #10592364 | C2 | semidirect |
| 18. #64083 | C4 | semidirect |
| 23. C3×#382 | D3 | semidirect |
| 36. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 37. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 41. C32×C42 | C2×C4 | semidirect |
| 45. C4×C3⋊Dic3 | D4 | semidirect |
| 84. #382 | C3⋊D3 | semidirect |
| 100. C3×C42 | C4×D3 | semidirect |
| 175. C42 | C4×C3⋊D3 | semidirect |
| 190. C32 | #2328 | semidirect |
| 230. C3 | #74153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64102 | 2 |
| C2×#64083 | 2 |
| C32×#382 | 2 |
| #10592687 | 2 |
| #10592631 | 2 |
| #10592364 | 2 |
| #74153 | 3 |