Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1330 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 188 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×D4×#157 | C2 | semidirect |
| 3. #10593827 | C2 | semidirect |
| 4. #10593826 | C2 | semidirect |
| 5. C4×C4⋊#157 | C2 | semidirect |
| 15. C32×#127 | C4 | semidirect |
| 16. #64149 | C4 | semidirect |
| 17. #64149 | C4 | semidirect |
| 18. #64083 | C4 | semidirect |
| 27. C2×C32×D4 | C2×C4 | semidirect |
| 28. C2×C32×D4 | C2×C4 | semidirect |
| 29. C2×#638 | C2×C4 | semidirect |
| 30. C2×#638 | C2×C4 | semidirect |
| 35. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 36. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 42. C4⋊#157 | D4 | semidirect |
| 44. C32×C42 | C2×C4 | semidirect |
| 45. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 46. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 119. C32×C4 | C4×D4 | semidirect |
| 121. C3⋊Dic3 | C4×D4 | semidirect |
| 128. #127 | #157 | semidirect |
| 174. C2×D4 | C2×#157 | semidirect |
| 175. C2×D4 | C2×#157 | semidirect |
| 189. C42 | C2×#157 | semidirect |
| 206. C32 | #2366 | semidirect |
| 259. C4 | D4×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C3⋊D3×#127 | 2 |
| #10593827 | 2 |
| #10593826 | 2 |
| C4×C4⋊#157 | 2 |
| #2366 | 9 |