Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1548 conjugacy classes of subgroups; only the 433 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 433 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. C32×C43 | C2 | semidirect |
| 5. #10592636 | C2 | semidirect |
| 6. #10592632 | C2 | semidirect |
| 7. C4×#3750 | C2 | semidirect |
| 18. #64085 | C4 | direct (N × H) |
| 24. C3×C43 | D3 | semidirect |
| 40. C32×C42 | C2×C4 | semidirect |
| 44. #3750 | C2×C4 | semidirect |
| 86. C43 | C3⋊D3 | semidirect |
| 97. C3×C42 | C4×D3 | semidirect |
| 111. C32×C4 | #126 | semidirect |
| 167. C42 | C4×C3⋊D3 | semidirect |
| 176. C3×C4 | #876 | semidirect |
| 180. C32 | C4×#126 | semidirect |
| 215. C4 | #64085 | direct (N × H) |
| 216. C3 | C4×#876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64085 | 2 |
| C32×C43 | 2 |
| #10592639 | 2 |
| C4×#3752 | 2 |
| #10592636 | 2 |
| #10592632 | 2 |
| C4×#3750 | 2 |
| C4×#876 | 3 |