Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
409 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 409 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 3. #10589106 | C2 | direct (N × H) |
| 10. C3×#812 | C4 | semidirect |
| 12. C2×C3×C3⋊C16 | C4 | semidirect |
| 29. C3×C3⋊C16 | C2×C4 | semidirect |
| 44. #812 | Dic3 | semidirect |
| 46. C2×C3⋊C16 | Dic3 | semidirect |
| 87. C3⋊C16 | C2×Dic3 | semidirect |
| 133. C2×C32 | #347 | semidirect |
| 165. C32 | C2×#347 | semidirect |
| 184. C2×C3 | #4512 | semidirect |
| 196. C3 | C2×#4512 | semidirect |
| 199. C2 | #10589106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63642 | 2 |
| C2×C3×#812 | 2 |
| #10589106 | 2 |
| C2×#4512 | 3 |