Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
265 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 90 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×C32×Q32 | C2 | semidirect |
| 3. C3×#4521 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊C32 | C2 | semidirect |
| 6. C2×#4521 | C3 | direct (N × H) |
| 10. C32×Q32 | C22 | semidirect |
| 14. C3×C3⋊C32 | C22 | semidirect |
| 16. C2×C3×Q32 | D3 | semidirect |
| 17. C2×C3×Q32 | C2×C3 | semidirect |
| 22. #4521 | C2×C3 | direct (N × H) |
| 23. C2×C3⋊C32 | C2×C3 | semidirect |
| 43. C3×Q32 | C2×D3 | semidirect |
| 44. C3×Q32 | C22×C3 | semidirect |
| 53. C3⋊C32 | C22×C3 | semidirect |
| 63. C2×Q32 | C3×D3 | semidirect |
| 100. Q32 | C2×C3×D3 | semidirect |
| 129. C2×C32 | SD64 | semidirect |
| 157. C32 | C2×SD64 | semidirect |
| 170. C2×C3 | #4521 | direct (N × H) |
| 171. C2×C3 | C3×SD64 | semidirect |
| 182. C3 | C2×#4521 | direct (N × H) |
| 183. C3 | C2×C3×SD64 | semidirect |
| 185. C2 | C3×#4521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C2×C3×D48 | 2 |
| C3×#4521 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C2×C3×SD64 | 3 |
| C2×#4521 | 3 |