Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 285 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×C4×M16 | C2 | semidirect |
| 4. C42×C3⋊Dic3 | C2 | semidirect |
| 5. #10589421 | C2 | semidirect |
| 14. C4×C4⋊(C3⋊D3) | C4 | semidirect |
| 17. C4×#634 | C4 | semidirect |
| 20. #63652 | C4 | direct (N × H) |
| 22. C3×C4×M16 | D3 | semidirect |
| 37. C32×M16 | C2×C4 | semidirect |
| 50. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 81. C4⋊(C3⋊D3) | C42 | semidirect |
| 85. #634 | C42 | semidirect |
| 89. C4×M16 | C3⋊D3 | semidirect |
| 103. C3×M16 | C4×D3 | semidirect |
| 123. C32×C4 | #104 | semidirect |
| 180. M16 | C4×C3⋊D3 | semidirect |
| 200. C3×C4 | #825 | semidirect |
| 207. C32 | C4×#104 | semidirect |
| 242. C4 | #63652 | direct (N × H) |
| 246. C3 | C4×#825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3828 | 2 |
| C32×C4×M16 | 2 |
| C2×#63652 | 2 |
| C42×C3⋊Dic3 | 2 |
| #10589421 | 2 |
| C4×#825 | 3 |